In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be est...In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.展开更多
In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of seconda...In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly due to correlated responses. Marginal models, such as generalized estimating equations (GEEs), have received much attention based on the assumption of the first two moments of the data and a working correlation structure. The confidence regions and hypothesis tests are constructed based on the asymptotic normality. This approach is sensitive to the misspecification of the variance function and the working correlation structure which may yield inefficient and inconsistent estimates leading to wrong conclusions. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its <span style="font-family:Verdana;">characteristics and asymptotic properties. We also provide an algorithm base</span><span style="font-family:Verdana;">d on EL principles for the estimation of the regression parameters and the construction of its confidence region. We have applied the proposed method in two case examples.</span>展开更多
Logic regression is an adaptive regression method which searches for Boolean (logic) combinations of binary variables that best explain the variability in the outcome, and thus, it reveals interaction effects which ar...Logic regression is an adaptive regression method which searches for Boolean (logic) combinations of binary variables that best explain the variability in the outcome, and thus, it reveals interaction effects which are associated with the response. In this study, we extended logic regression to longitudinal data with binary response and proposed “Transition Logic Regression Method” to find interactions related to response. In this method, interaction effects over time were found by Annealing Algorithm with AIC (Akaike Information Criterion) as the score function of the model. Also, first and second orders Markov dependence were allowed to capture the correlation among successive observations of the same individual in longitudinal binary response. Performance of the method was evaluated with simulation study in various conditions. Proposed method was used to find interactions of SNPs and other risk factors related to low HDL over time in data of 329 participants of longitudinal TLGS study.展开更多
In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under so...In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.展开更多
Prediction plays an important role in data analysis.Model averaging method generally provides better prediction than using any of its components.Even though model averaging has been extensively investigated under inde...Prediction plays an important role in data analysis.Model averaging method generally provides better prediction than using any of its components.Even though model averaging has been extensively investigated under independent errors,few authors have considered model averaging for semiparametric models with correlated errors.In this paper,the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal data.The model averaging weights are obtained by minimizing criterion,which is an unbiased estimator of the expected in-sample squared error loss plus a constant.Asymptotic properties,including asymptotic optimality and consistency of averaging weights,are established under two scenarios:(i)All candidate models are misspecified;(ii)Correct models are available in the candidate set.Simulation studies and an empirical example show that the promise of the proposed procedure over other competitive methods.展开更多
Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longit...Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.展开更多
Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigat...Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.展开更多
Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper ...Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data.The proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant coefficients.It is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient models.Under regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients.The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically normal.Finally,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis.The results show that the proposed method performs better than the existing competitor.展开更多
A partially linear model with longitudinal data is considered, empirical likelihood to infer- ence for the regression coefficients and the baseline function is investigated, the empirical log-likelihood ratios is prov...A partially linear model with longitudinal data is considered, empirical likelihood to infer- ence for the regression coefficients and the baseline function is investigated, the empirical log-likelihood ratios is proven to be asymptotically chi-squared, and the corresponding confidence regions for the pa- rameters of interest are then constructed. Also by the empirical likelihood ratio functions, we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function, and prove the asymptotic normality. The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method, and a real example is analysed.展开更多
In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the mode...In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.展开更多
Model average receives much attention in recent years.This paper considers the semiparametric model averaging for high-dimensional longitudinal data.To minimize the prediction error,the authors estimate the model weig...Model average receives much attention in recent years.This paper considers the semiparametric model averaging for high-dimensional longitudinal data.To minimize the prediction error,the authors estimate the model weights using a leave-subject-out cross-validation procedure.Asymptotic optimality of the proposed method is proved in the sense that leave-subject-out cross-validation achieves the lowest possible prediction loss asymptotically.Simulation studies show that the performance of the proposed model average method is much better than that of some commonly used model selection and averaging methods.展开更多
Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions...Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.展开更多
Modeling the mean and covariance simultaneously is a common strategy to efficiently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data. In this article, using ge...Modeling the mean and covariance simultaneously is a common strategy to efficiently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data. In this article, using generalized estimation equation techniques, we propose a new kind of regression models for parameterizing covariance structures. Using a novel Cholesky factor, the entries in this decomposition have moving average and log innovation interpretation and are modeled as the regression coefficients in both the mean and the linear functions of covariates. The resulting estimators for eovarianee are shown to be consistent and asymptotically normally distributed. Simulation studies and a real data analysis show that the proposed approach yields highly efficient estimators for the parameters in the mean, and provides parsimonious estimation for the covariance structure.展开更多
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asy...In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.展开更多
In this paper we use profile empirical likelihood to construct confidence regions for regression coefficients in partially linear model with longitudinal data. The main contribution is that the within-subject correlat...In this paper we use profile empirical likelihood to construct confidence regions for regression coefficients in partially linear model with longitudinal data. The main contribution is that the within-subject correlation is considered to improve estimation efficiency. We suppose a semi-parametric structure for the covariances of observation errors in each subject and employ both the first order and the second order moment conditions of the observation errors to construct the estimating equations. Although there are nonparametric variable in distribution after estimators, the empirical log-likelihood ratio statistic still tends to a standard Xp2 the nuisance parameters are profiled away. A data simulation is also conducted.展开更多
In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, d...In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.展开更多
Empirical likelihood inference for partially linear errors-in-variables models with longitudinal data is investigated.Under regularity conditions,it is shown that the empirical log-likelihood ratio at the true paramet...Empirical likelihood inference for partially linear errors-in-variables models with longitudinal data is investigated.Under regularity conditions,it is shown that the empirical log-likelihood ratio at the true parameters converges to the standard Chi-squared distribution.Furthermore,we consider some estimates of the unknown parameter and the resulting estimators are shown to be asymptotically normal.Some simulations and a real data analysis are given to illustrate the performance of the proposed method.展开更多
For left censored response longitudinal data, we propose a composite quantile regression estimator(CQR) of regression parameter. Statistical properties such as consistency and asymptotic normality of CQR are studied...For left censored response longitudinal data, we propose a composite quantile regression estimator(CQR) of regression parameter. Statistical properties such as consistency and asymptotic normality of CQR are studied under relaxable assumptions of correlation structure of error terms. The performance of CQR is investigated via simulation studies and a real dataset analysis.展开更多
Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estim...Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.展开更多
The method of generalized estimating equations (GEE) introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect ag...The method of generalized estimating equations (GEE) introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. In this paper, we present a new method named as 'weighted estimating equations (WEE)' for estimating the correlation parameters. The new estimates of correlation parameters are obtained as the solutions of these weighted estimating equations. For some commonly assumed correlation structures, we show that there exists a unique feasible solution to these weighted estimating equations regardless the correlation structure is correctly specified or not. The new feasible estimates of correlation parameters are consistent when the working correlation structure is correctly specified. Simulation results suggest that the new method works well in finite samples.展开更多
基金Supported by the National Natural Science Foundation of China (10571008)the Natural Science Foundation of Henan (092300410149)the Core Teacher Foundationof Henan (2006141)
文摘In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.
文摘In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly due to correlated responses. Marginal models, such as generalized estimating equations (GEEs), have received much attention based on the assumption of the first two moments of the data and a working correlation structure. The confidence regions and hypothesis tests are constructed based on the asymptotic normality. This approach is sensitive to the misspecification of the variance function and the working correlation structure which may yield inefficient and inconsistent estimates leading to wrong conclusions. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its <span style="font-family:Verdana;">characteristics and asymptotic properties. We also provide an algorithm base</span><span style="font-family:Verdana;">d on EL principles for the estimation of the regression parameters and the construction of its confidence region. We have applied the proposed method in two case examples.</span>
文摘Logic regression is an adaptive regression method which searches for Boolean (logic) combinations of binary variables that best explain the variability in the outcome, and thus, it reveals interaction effects which are associated with the response. In this study, we extended logic regression to longitudinal data with binary response and proposed “Transition Logic Regression Method” to find interactions related to response. In this method, interaction effects over time were found by Annealing Algorithm with AIC (Akaike Information Criterion) as the score function of the model. Also, first and second orders Markov dependence were allowed to capture the correlation among successive observations of the same individual in longitudinal binary response. Performance of the method was evaluated with simulation study in various conditions. Proposed method was used to find interactions of SNPs and other risk factors related to low HDL over time in data of 329 participants of longitudinal TLGS study.
基金the Natural Science Foundation of China(10371042,10671038)
文摘In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.
基金supported by the National Natural Science Foundation of China under Grant Nos.11971421,71925007,72091212,and 12288201Yunling Scholar Research Fund of Yunnan Province under Grant No.YNWR-YLXZ-2018-020+1 种基金the CAS Project for Young Scientists in Basic Research under Grant No.YSBR-008the Start-Up Grant from Kunming University of Science and Technology under Grant No.KKZ3202207024.
文摘Prediction plays an important role in data analysis.Model averaging method generally provides better prediction than using any of its components.Even though model averaging has been extensively investigated under independent errors,few authors have considered model averaging for semiparametric models with correlated errors.In this paper,the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal data.The model averaging weights are obtained by minimizing criterion,which is an unbiased estimator of the expected in-sample squared error loss plus a constant.Asymptotic properties,including asymptotic optimality and consistency of averaging weights,are established under two scenarios:(i)All candidate models are misspecified;(ii)Correct models are available in the candidate set.Simulation studies and an empirical example show that the promise of the proposed procedure over other competitive methods.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11922117,11771361)Fujian Provincial Science Fund for Distinguished Young Scholars(Grant No.2019J06004)。
文摘Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.
基金supported by the Natural Science Foundation of China under Grant Nos.12031016,11061002,11801033,12071014 and 12131001the National Social Science Fund of China under Grant No.19ZDA121the Natural Science Foundation of Guangxi under Grant Nos.2015GXNSFAA139006 and LMEQF。
文摘Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.
基金supported in part by the National Science Foundation of China under Grant Nos.12071305and 71803001in part by the national social science foundation of China under Grant No.19BTJ014+1 种基金in part by the University Social Science Research Project of Anhui Province under Grant No.SK2020A0051in part by the Social Science Foundation of the Ministry of Education of China under Grant Nos.19YJCZH250 and 21YJAZH081。
文摘Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data.The proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant coefficients.It is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient models.Under regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients.The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically normal.Finally,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis.The results show that the proposed method performs better than the existing competitor.
基金The first author was supported by the National Natural Science Foundation of China (Grant No. 10571008)the Natural Science Foundation of Beijing (Grant No. 1072004)+1 种基金the Science and Technology Development Project of Education Committee of Beijing City (Grant No. KM200510005009)The second author was supported by a grant of the Research Grant Council of Hong Kong (Grant No. HKBU7060/04P)
文摘A partially linear model with longitudinal data is considered, empirical likelihood to infer- ence for the regression coefficients and the baseline function is investigated, the empirical log-likelihood ratios is proven to be asymptotically chi-squared, and the corresponding confidence regions for the pa- rameters of interest are then constructed. Also by the empirical likelihood ratio functions, we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function, and prove the asymptotic normality. The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method, and a real example is analysed.
基金China Postdoctoral Science Foundation Funded Project (20080430633)Shanghai Postdoctoral Scientific Program (08R214121)+3 种基金the National Natural Science Foundation of China (10871013)the Research Fund for the Doctoral Program of Higher Education (20070005003)the Natural Science Foundation of Beijing (1072004)the Basic Research and Frontier Technology Foundation of He'nan (072300410090)
文摘In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.
基金the Ministry of Science and Technology of China under Grant No.2016YFB0502301Academy for Multidisciplinary Studies of Capital Normal University,and the National Natural Science Foundation of China under Grant Nos.11971323 and 11529101。
文摘Model average receives much attention in recent years.This paper considers the semiparametric model averaging for high-dimensional longitudinal data.To minimize the prediction error,the authors estimate the model weights using a leave-subject-out cross-validation procedure.Asymptotic optimality of the proposed method is proved in the sense that leave-subject-out cross-validation achieves the lowest possible prediction loss asymptotically.Simulation studies show that the performance of the proposed model average method is much better than that of some commonly used model selection and averaging methods.
基金Research Foundation for Doctor Programme (Grant No.20060254006)the National Natural Science Foundation of China (Grant No.10671089)
文摘Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.
基金supported by National Natural Science Foundation of China(Grant Nos.11271347 and 11171321)
文摘Modeling the mean and covariance simultaneously is a common strategy to efficiently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data. In this article, using generalized estimation equation techniques, we propose a new kind of regression models for parameterizing covariance structures. Using a novel Cholesky factor, the entries in this decomposition have moving average and log innovation interpretation and are modeled as the regression coefficients in both the mean and the linear functions of covariates. The resulting estimators for eovarianee are shown to be consistent and asymptotically normally distributed. Simulation studies and a real data analysis show that the proposed approach yields highly efficient estimators for the parameters in the mean, and provides parsimonious estimation for the covariance structure.
基金supported by National Natural Science Foundation of China (Grant Nos.10671038,10801039)Youth Science Foundation of Fudan University (Grant No.08FQ29)Shanghai Leading Academic Discipline Project (Grant No.B118)
文摘In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.
基金Supported by NBRP (973 Program 2007CB814901) of ChinaNNSF project (10771123) of China+1 种基金RFDP(20070422034) of ChinaNSF projects (ZR2010AZ001) of Shandong Province of China
文摘In this paper we use profile empirical likelihood to construct confidence regions for regression coefficients in partially linear model with longitudinal data. The main contribution is that the within-subject correlation is considered to improve estimation efficiency. We suppose a semi-parametric structure for the covariances of observation errors in each subject and employ both the first order and the second order moment conditions of the observation errors to construct the estimating equations. Although there are nonparametric variable in distribution after estimators, the empirical log-likelihood ratio statistic still tends to a standard Xp2 the nuisance parameters are profiled away. A data simulation is also conducted.
基金Supported by National Natural Science Foundation of China(Grant Nos.11501522,11101014,11001118 and11171012)National Statistical Research Projects(Grant No.2014LZ45)+2 种基金the Doctoral Fund of Innovation of Beijing University of Technologythe Science and Technology Project of the Faculty Adviser of Excellent PhD Degree Thesis of Beijing(Grant No.20111000503)the Beijing Municipal Education Commission Foundation(Grant No.KM201110005029)
文摘In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.
基金Supported by the State Key Program of National Natural Science Foundation of China(No.12031016)the National Natural Science Foundation of China(No.11801346)+2 种基金the Youth Fund for Humanities and Social Sciences Research of Ministry of Education(No.18YJC910014)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2020JM-276)the Fundamental Research Funds for the Central Universities(No.GK201901008)。
文摘Empirical likelihood inference for partially linear errors-in-variables models with longitudinal data is investigated.Under regularity conditions,it is shown that the empirical log-likelihood ratio at the true parameters converges to the standard Chi-squared distribution.Furthermore,we consider some estimates of the unknown parameter and the resulting estimators are shown to be asymptotically normal.Some simulations and a real data analysis are given to illustrate the performance of the proposed method.
基金Supported in part by the National Natural Science Foundation of China under(Grant No.11601097 and 11471302)the State Key Program of National Natural Science of China(Grant No.11231010)
文摘For left censored response longitudinal data, we propose a composite quantile regression estimator(CQR) of regression parameter. Statistical properties such as consistency and asymptotic normality of CQR are studied under relaxable assumptions of correlation structure of error terms. The performance of CQR is investigated via simulation studies and a real dataset analysis.
基金Supported by National Natural Science Foundation of China(Grant No.11101119)the Training Program for Excellent Young Teachers in Guangxi Universitiesthe Philosophy and Social Sciences Foundation of Guangxi(Grant No.11FTJ002)
文摘Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.
文摘The method of generalized estimating equations (GEE) introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. In this paper, we present a new method named as 'weighted estimating equations (WEE)' for estimating the correlation parameters. The new estimates of correlation parameters are obtained as the solutions of these weighted estimating equations. For some commonly assumed correlation structures, we show that there exists a unique feasible solution to these weighted estimating equations regardless the correlation structure is correctly specified or not. The new feasible estimates of correlation parameters are consistent when the working correlation structure is correctly specified. Simulation results suggest that the new method works well in finite samples.