A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kin...A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.展开更多
The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is...The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.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
In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing respo...In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.展开更多
The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron's resampling technique, and the...The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron's resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.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
In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong ...In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.展开更多
This paper proposes an empirical likelihood based diagnostic technique for heteroscedasticity for semiparametric varying-coefficient partially linear models with missing responses. Firstly, the authors complement the ...This paper proposes an empirical likelihood based diagnostic technique for heteroscedasticity for semiparametric varying-coefficient partially linear models with missing responses. Firstly, the authors complement the missing response variables by regression method. Then, the empirical likelihood method is introduced to study the heteroscedasticity of the semiparametric varying-coefficient partially linear models with complete-case data. Finally, the authors obtain the finite sample property by numerical simulation.展开更多
Panel count data are frequently encountered when study subjects are under discrete observations.However,limited literature has been found on variable selection for panel count data.In this paper,without considering th...Panel count data are frequently encountered when study subjects are under discrete observations.However,limited literature has been found on variable selection for panel count data.In this paper,without considering the model assumption of observation process,a more general semiparametric transformation model for panel count data with informative observation process is developed.A penalized estimation procedure based on the quantile regression function is proposed for variable selection and parameter estimation simultaneously.The consistency and oracle properties of the estimators are established under some mild conditions.Some simulations and an application are reported to evaluate the proposed approach.展开更多
Consider a semiparametric regression model Y_i=X_iβ+g(t_i)+e_i, 1 ≤ i ≤ n, where Y_i is censored on the right by another random variable C_i with known or unknown distribution G. The wavelet estimators of param...Consider a semiparametric regression model Y_i=X_iβ+g(t_i)+e_i, 1 ≤ i ≤ n, where Y_i is censored on the right by another random variable C_i with known or unknown distribution G. The wavelet estimators of parameter and nonparametric part are given by the wavelet smoothing and the synthetic data methods. Under general conditions, the asymptotic normality for the wavelet estimators and the convergence rates for the wavelet estimators of nonparametric components are investigated. A numerical example is given.展开更多
We consider the semiparametric partially linear regression models with mean function XTβ + g(z), where X and z are functional data. The new estimators of β and g(z) are presented and some asymptotic results are...We consider the semiparametric partially linear regression models with mean function XTβ + g(z), where X and z are functional data. The new estimators of β and g(z) are presented and some asymptotic results are given. The strong convergence rates of the proposed estimators are obtained. In our estimation, the observation number of each subject will be completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.展开更多
In view of the influence of model errors in conventional BeiDou prediction models for clock offsets,a semiparametric adjustment model for BeiDou Navigation Satellite System(BDS)clock offset prediction that considers m...In view of the influence of model errors in conventional BeiDou prediction models for clock offsets,a semiparametric adjustment model for BeiDou Navigation Satellite System(BDS)clock offset prediction that considers model errors is proposed in this paper.First,the model errors of the conventional BeiDou clock offset prediction model are analyzed.Additionally,the relationship among the polynomial model,polynomial model with additional periodic term correction,and its periodic correction terms is explored in detail.Second,considering the model errors,combined with the physical relationship between phase,frequency,frequency drift,and its period in the clock sequence,the conventional clock offset prediction model is improved.Using kernel estimation and comprehensive least squares,the corresponding parameter solutions of the prediction model and the estimation of its model error are derived,and the dynamic error correction of the clock sequence model is realized.Finally,the BDS satellite precision clock data provided by the IGS Center of Wuhan University with a sampling interval of 5 min are used to compare the proposed prediction method with commonly used methods.Experimental results show that the proposed prediction method can better correct the model errors of BDS satellite clock offsets,and it can effectively overcome the inaccuracies of clock offset correction.The average forecast accuracies of the BeiDou satellites at 6,12,and 24 h are 27.13%,37.71%,and 45.08%higher than those of the conventional BeiDou clock offset forecast models;the average model improvement rates are 16.92%,20.96%,and 28.48%,respectively.In addition,the proposed method enhances the existing BDS satellite prediction method for clock offsets to a certain extent.展开更多
Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effect...Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors.However,these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data.Quantile regression is an ideal alternative to deal with these problems,as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust.In this paper,we consider Bayesian quantile regression analysis for semiparamet-ric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors.We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior dis-tributions to conduct the posterior inference.The performance of the proposed procedure is evaluated through simulation studies and a real data application.展开更多
In this article we study a semiparametric mixture model for the two-sample problem with right censored data. The model implies that the densities for the continuous outcomes are related by a parametric tilt but otherw...In this article we study a semiparametric mixture model for the two-sample problem with right censored data. The model implies that the densities for the continuous outcomes are related by a parametric tilt but otherwise unspecified. It provides a useful alternative to the Cox (1972) proportional hazards model for the comparison of treatments based on right censored survival data. We propose an iterative algorithm for the semiparametric maximum likelihood estimates of the parametric and nonparametric components of the model. The performance of the proposed method is studied using simulation. We illustrate our method in an application to melanoma.展开更多
Joint parsimonious modeling the mean and covariance is important for analyzing longitudinal data,because it accounts for the efficiency of parameter estimation and easy interpretation of variability.The main potential...Joint parsimonious modeling the mean and covariance is important for analyzing longitudinal data,because it accounts for the efficiency of parameter estimation and easy interpretation of variability.The main potential risk is that it may lead to inefficient or biased estimators of parameters while misspecification occurs.A good alternative is the semiparametric model.In this paper,a Bayesian approach is proposed for modeling the mean and covariance simultaneously by using semiparametric models and the modified Cholesky decomposition.We use a generalized prior to avoid the knots selection while using B-spline to approximate the nonlinear part and propose a Markov Chain Monte Carlo scheme based on Metropolis–Hastings algorithm for computations.Simulation studies and real data analysis show that the proposed approach yields highly efficient estimators for the parameters and nonparametric parts in the mean,meanwhile providing parsimonious estimation for the covariance structure.展开更多
For the semiparametric regression model:Y^((j))(x_(in),t_(in))=t_(in)β+g(x_(in))+e^((j))(x_(in)),1≤j≤k,1≤i≤n,where t_(in)∈R and x(in)∈Rpare known to be nonrandom,g is an unknown continuous function on a compact...For the semiparametric regression model:Y^((j))(x_(in),t_(in))=t_(in)β+g(x_(in))+e^((j))(x_(in)),1≤j≤k,1≤i≤n,where t_(in)∈R and x(in)∈Rpare known to be nonrandom,g is an unknown continuous function on a compact set A in R^(p),e^(j)(x_(in))are m-extended negatively dependent random errors with mean zero,Y^((j))(x_(in),t_(in))represent the j-th response variables which are observable at points xin,tin.In this paper,we study the strong consistency,complete consistency and r-th(r>1)mean consistency for the estimatorsβ_(k,n)and g__(k,n)ofβand g,respectively.The results obtained in this paper markedly improve and extend the corresponding ones for independent random variables,negatively associated random variables and other mixing random variables.Moreover,we carry out a numerical simulation for our main results.展开更多
In this paper. the authors consider Bahadur asymptotic efficiency of LS estimators βof β, which is an unknown parameter vector in the semiparametric regression model Y=HTβ+g(T)+ε,where g is an unknown Holder conti...In this paper. the authors consider Bahadur asymptotic efficiency of LS estimators βof β, which is an unknown parameter vector in the semiparametric regression model Y=HTβ+g(T)+ε,where g is an unknown Holder continuous function, ε is a random error, X is a random vector in Rk, T is a random variable in [0,1], X and T are independent.展开更多
The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum pena...The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.展开更多
Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient esti...Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient estimator of β is constructed on the basis of the model Yi=Xτiβ+g(Ti)+εi, i=1,…,n, when the density functions of (X,T) and ε are known or unknown.Finally, an asymptotically normal estimator of σ2 is given.展开更多
This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ+Zτiα(Ui)+εi , Wi=Xi+ξi,i=1, · · · , n. Due to me...This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ+Zτiα(Ui)+εi , Wi=Xi+ξi,i=1, · · · , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.展开更多
文摘A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.
基金Supported by the Natural Science Foundation of Jiangsu Province (BK2008284)
文摘The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.
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Supported by National Natural Science Foundation of China (Grant No. 10871013), Natural Science Foundation of Beijing (Grant No. 1072004), and Natural Science Foundation of Guangxi Province (Grant No. 2010GXNSFB013051)
文摘In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10571008, 10871013)Beijing Natural Science Foundation (Grant No. 1072004)Ph.D. Program Foundation of Ministry of Education of China (Grant No. 20070005003)
文摘The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron's resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.
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Supported by the Natural Science Foundation of Beijing City of China (1042002)the Science and Technology Development Foundation of Education Committee of Beijing Citythe Special Expenditure of Excellent Person Education of Beijing(20041D0501515)
文摘In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.
基金supported by the National Natural Science Foundation of China under Grant Nos. 11471060 and 11871124the Key Project of Statistical Science of China under Grant No. 2017LZ27。
文摘This paper proposes an empirical likelihood based diagnostic technique for heteroscedasticity for semiparametric varying-coefficient partially linear models with missing responses. Firstly, the authors complement the missing response variables by regression method. Then, the empirical likelihood method is introduced to study the heteroscedasticity of the semiparametric varying-coefficient partially linear models with complete-case data. Finally, the authors obtain the finite sample property by numerical simulation.
基金partially supported by the National Natural Science Foundation of China under Grant No.12001485the National Bureau of Statistics of China under Grant No.2020LY073the First Class Discipline of Zhejiang-A(Zhejiang University of Finance and Economics-Statistics)under Grant No.Z0111119010/024。
文摘Panel count data are frequently encountered when study subjects are under discrete observations.However,limited literature has been found on variable selection for panel count data.In this paper,without considering the model assumption of observation process,a more general semiparametric transformation model for panel count data with informative observation process is developed.A penalized estimation procedure based on the quantile regression function is proposed for variable selection and parameter estimation simultaneously.The consistency and oracle properties of the estimators are established under some mild conditions.Some simulations and an application are reported to evaluate the proposed approach.
基金Supported by the National Natural Science Foundation of China (11071022)the Key Project of Hubei Provincial Department of Education (D20092207)
文摘Consider a semiparametric regression model Y_i=X_iβ+g(t_i)+e_i, 1 ≤ i ≤ n, where Y_i is censored on the right by another random variable C_i with known or unknown distribution G. The wavelet estimators of parameter and nonparametric part are given by the wavelet smoothing and the synthetic data methods. Under general conditions, the asymptotic normality for the wavelet estimators and the convergence rates for the wavelet estimators of nonparametric components are investigated. A numerical example is given.
文摘We consider the semiparametric partially linear regression models with mean function XTβ + g(z), where X and z are functional data. The new estimators of β and g(z) are presented and some asymptotic results are given. The strong convergence rates of the proposed estimators are obtained. In our estimation, the observation number of each subject will be completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.
基金China University of Geosciences,Wuhan(CN)(Grant No.41374017).
文摘In view of the influence of model errors in conventional BeiDou prediction models for clock offsets,a semiparametric adjustment model for BeiDou Navigation Satellite System(BDS)clock offset prediction that considers model errors is proposed in this paper.First,the model errors of the conventional BeiDou clock offset prediction model are analyzed.Additionally,the relationship among the polynomial model,polynomial model with additional periodic term correction,and its periodic correction terms is explored in detail.Second,considering the model errors,combined with the physical relationship between phase,frequency,frequency drift,and its period in the clock sequence,the conventional clock offset prediction model is improved.Using kernel estimation and comprehensive least squares,the corresponding parameter solutions of the prediction model and the estimation of its model error are derived,and the dynamic error correction of the clock sequence model is realized.Finally,the BDS satellite precision clock data provided by the IGS Center of Wuhan University with a sampling interval of 5 min are used to compare the proposed prediction method with commonly used methods.Experimental results show that the proposed prediction method can better correct the model errors of BDS satellite clock offsets,and it can effectively overcome the inaccuracies of clock offset correction.The average forecast accuracies of the BeiDou satellites at 6,12,and 24 h are 27.13%,37.71%,and 45.08%higher than those of the conventional BeiDou clock offset forecast models;the average model improvement rates are 16.92%,20.96%,and 28.48%,respectively.In addition,the proposed method enhances the existing BDS satellite prediction method for clock offsets to a certain extent.
基金Dr.Wu was supported by the National Natural Science Foundation of China under grant 11861041Drs.Keying Ye and Min Wang were partially supported by a grant from the UTSA Vice President for Research,Economic Development,and Knowledge Enterprise at the University of Texas at San Antonio.
文摘Semiparametric mixed-effects double regression models have been used for analysis of longitu-dinal data in a variety of applications,as they allow researchers to jointly model the mean and variance of the mixed-effects as a function of predictors.However,these models are commonly estimated based on the normality assumption for the errors and the results may thus be sensitive to outliers and/or heavy-tailed data.Quantile regression is an ideal alternative to deal with these problems,as it is insensitive to heteroscedasticity and outliers and can make statistical analysis more robust.In this paper,we consider Bayesian quantile regression analysis for semiparamet-ric mixed-effects double regression models based on the asymmetric Laplace distribution for the errors.We construct a Bayesian hierarchical model and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full posterior dis-tributions to conduct the posterior inference.The performance of the proposed procedure is evaluated through simulation studies and a real data application.
基金supported in part by the U.S.National Institute of Health(No.CA016042,No.P01AT003960)Chien-Tai Lin's research was supported in part by the National Science Council of Taiwan(No.89-2118-M-032-021,No.96-2628-M-032-002-MY3)
文摘In this article we study a semiparametric mixture model for the two-sample problem with right censored data. The model implies that the densities for the continuous outcomes are related by a parametric tilt but otherwise unspecified. It provides a useful alternative to the Cox (1972) proportional hazards model for the comparison of treatments based on right censored survival data. We propose an iterative algorithm for the semiparametric maximum likelihood estimates of the parametric and nonparametric components of the model. The performance of the proposed method is studied using simulation. We illustrate our method in an application to melanoma.
基金supported by the National Key Research and Development Plan(No.2016YFC0800100)the NSF of China(Nos.11671374,71631006).
文摘Joint parsimonious modeling the mean and covariance is important for analyzing longitudinal data,because it accounts for the efficiency of parameter estimation and easy interpretation of variability.The main potential risk is that it may lead to inefficient or biased estimators of parameters while misspecification occurs.A good alternative is the semiparametric model.In this paper,a Bayesian approach is proposed for modeling the mean and covariance simultaneously by using semiparametric models and the modified Cholesky decomposition.We use a generalized prior to avoid the knots selection while using B-spline to approximate the nonlinear part and propose a Markov Chain Monte Carlo scheme based on Metropolis–Hastings algorithm for computations.Simulation studies and real data analysis show that the proposed approach yields highly efficient estimators for the parameters and nonparametric parts in the mean,meanwhile providing parsimonious estimation for the covariance structure.
基金supported by the National Natural Science Foundation of China(11671012,11871072)the Natural Science Foundation of Anhui Province(1808085QA03,1908085QA01,1908085QA07)the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0003)。
文摘For the semiparametric regression model:Y^((j))(x_(in),t_(in))=t_(in)β+g(x_(in))+e^((j))(x_(in)),1≤j≤k,1≤i≤n,where t_(in)∈R and x(in)∈Rpare known to be nonrandom,g is an unknown continuous function on a compact set A in R^(p),e^(j)(x_(in))are m-extended negatively dependent random errors with mean zero,Y^((j))(x_(in),t_(in))represent the j-th response variables which are observable at points xin,tin.In this paper,we study the strong consistency,complete consistency and r-th(r>1)mean consistency for the estimatorsβ_(k,n)and g__(k,n)ofβand g,respectively.The results obtained in this paper markedly improve and extend the corresponding ones for independent random variables,negatively associated random variables and other mixing random variables.Moreover,we carry out a numerical simulation for our main results.
文摘In this paper. the authors consider Bahadur asymptotic efficiency of LS estimators βof β, which is an unknown parameter vector in the semiparametric regression model Y=HTβ+g(T)+ε,where g is an unknown Holder continuous function, ε is a random error, X is a random vector in Rk, T is a random variable in [0,1], X and T are independent.
基金Supported by the National Natural Science Foundation of China (No. 10961026, 10761011)the National Social Science Foundation of China (No. 10BTJ001)
文摘The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM) which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models. Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented. Assessment of local influence for various perturbation schemes are investigated. Some local influence diagnostics are given. A simulation study and a real example are used to illustrate the proposed methodologies.
文摘Consider the model Y=Xτβ+g(T)+ε. Here g is a smooth but unknown function, β is a k×1 parameter vector to be estimated and ε, is an random error with mean 0 and variance σ2. The asymptotically efficient estimator of β is constructed on the basis of the model Yi=Xτiβ+g(Ti)+εi, i=1,…,n, when the density functions of (X,T) and ε are known or unknown.Finally, an asymptotically normal estimator of σ2 is given.
基金supported by National Natural Science Funds for Distinguished Young Scholar(No.70825004) and (No.71271128)Creative Research Groups of China(No.71271128)+1 种基金NCMIS and Shanghai University of Finance and Economics through Project 211 Phase ⅢShanghai Leading Academic Discipline Project(No.B803)
文摘This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ+Zτiα(Ui)+εi , Wi=Xi+ξi,i=1, · · · , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.