Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and varianc...Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.展开更多
Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobse...Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).展开更多
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
Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Mulle...Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.展开更多
Medical research data are often skewed and heteroscedastic. It has therefore become practice to log-transform data in regression analysis, in order to stabilize the variance. Regression analysis on log-transformed dat...Medical research data are often skewed and heteroscedastic. It has therefore become practice to log-transform data in regression analysis, in order to stabilize the variance. Regression analysis on log-transformed data estimates the relative effect, whereas it is often the absolute effect of a predictor that is of interest. We propose a maximum likelihood (ML)-based approach to estimate a linear regression model on log-normal, heteroscedastic data. The new method was evaluated with a large simulation study. Log-normal observations were generated according to the simulation models and parameters were estimated using the new ML method, ordinary least-squares regression (LS) and weighed least-squares regression (WLS). All three methods produced unbiased estimates of parameters and expected response, and ML and WLS yielded smaller standard errors than LS. The approximate normality of the Wald statistic, used for tests of the ML estimates, in most situations produced correct type I error risk. Only ML and WLS produced correct confidence intervals for the estimated expected value. ML had the highest power for tests regarding β1.展开更多
The development of many estimators of parameters of linear regression model is traceable to non-validity of the assumptions under which the model is formulated, especially when applied to real life situation. This not...The development of many estimators of parameters of linear regression model is traceable to non-validity of the assumptions under which the model is formulated, especially when applied to real life situation. This notwithstanding, regression analysis may aim at prediction. Consequently, this paper examines the performances of the Ordinary Least Square (OLS) estimator, Cochrane-Orcutt (COR) estimator, Maximum Likelihood (ML) estimator and the estimators based on Principal Component (PC) analysis in prediction of linear regression model under the joint violations of the assumption of non-stochastic regressors, independent regressors and error terms. With correlated stochastic normal variables as regressors and autocorrelated error terms, Monte-Carlo experiments were conducted and the study further identifies the best estimator that can be used for prediction purpose by adopting the goodness of fit statistics of the estimators. From the results, it is observed that the performances of COR at each level of correlation (multicollinearity) and that of ML, especially when the sample size is large, over the levels of autocorrelation have a convex-like pattern while that of OLS and PC are concave-like. Also, as the levels of multicollinearity increase, the estimators, except the PC estimators when multicollinearity is negative, rapidly perform better over the levels autocorrelation. The COR and ML estimators are generally best for prediction in the presence of multicollinearity and autocorrelated error terms. However, at low levels of autocorrelation, the OLS estimator is either best or competes consistently with the best estimator, while the PC estimator is either best or competes with the best when multicollinearity level is high(λ>0.8 or λ-0.49).展开更多
The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and deca...The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.展开更多
The capital asset pricing model (CAPM) is a commonly used regression model in finance to model stock returns. Bayesian methods have been developed for the CAPM to account for market fluctuations within the industry. H...The capital asset pricing model (CAPM) is a commonly used regression model in finance to model stock returns. Bayesian methods have been developed for the CAPM to account for market fluctuations within the industry. However, a Bayesian model checking procedure is needed to assess the CAPM in terms of the usual regression model assumptions of independence, homogeneity of variance, and normality. This paper develops Bayesian residuals and Bayesian p-values to check these model assumptions as well as to suggest model extensions to the CAPM.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is as...For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.展开更多
In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=...In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.展开更多
Consider the standard linear model where x<sub>x</sub>,x<sub>2</sub>… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e<sub>1</sub>, ...Consider the standard linear model where x<sub>x</sub>,x<sub>2</sub>… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e<sub>1</sub>, e<sub>2</sub>, …the independent random error sequence, each having a median zero. Define the minimum L<sub>1</sub>norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:展开更多
文摘Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.
文摘Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).
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Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.
文摘Medical research data are often skewed and heteroscedastic. It has therefore become practice to log-transform data in regression analysis, in order to stabilize the variance. Regression analysis on log-transformed data estimates the relative effect, whereas it is often the absolute effect of a predictor that is of interest. We propose a maximum likelihood (ML)-based approach to estimate a linear regression model on log-normal, heteroscedastic data. The new method was evaluated with a large simulation study. Log-normal observations were generated according to the simulation models and parameters were estimated using the new ML method, ordinary least-squares regression (LS) and weighed least-squares regression (WLS). All three methods produced unbiased estimates of parameters and expected response, and ML and WLS yielded smaller standard errors than LS. The approximate normality of the Wald statistic, used for tests of the ML estimates, in most situations produced correct type I error risk. Only ML and WLS produced correct confidence intervals for the estimated expected value. ML had the highest power for tests regarding β1.
文摘The development of many estimators of parameters of linear regression model is traceable to non-validity of the assumptions under which the model is formulated, especially when applied to real life situation. This notwithstanding, regression analysis may aim at prediction. Consequently, this paper examines the performances of the Ordinary Least Square (OLS) estimator, Cochrane-Orcutt (COR) estimator, Maximum Likelihood (ML) estimator and the estimators based on Principal Component (PC) analysis in prediction of linear regression model under the joint violations of the assumption of non-stochastic regressors, independent regressors and error terms. With correlated stochastic normal variables as regressors and autocorrelated error terms, Monte-Carlo experiments were conducted and the study further identifies the best estimator that can be used for prediction purpose by adopting the goodness of fit statistics of the estimators. From the results, it is observed that the performances of COR at each level of correlation (multicollinearity) and that of ML, especially when the sample size is large, over the levels of autocorrelation have a convex-like pattern while that of OLS and PC are concave-like. Also, as the levels of multicollinearity increase, the estimators, except the PC estimators when multicollinearity is negative, rapidly perform better over the levels autocorrelation. The COR and ML estimators are generally best for prediction in the presence of multicollinearity and autocorrelated error terms. However, at low levels of autocorrelation, the OLS estimator is either best or competes consistently with the best estimator, while the PC estimator is either best or competes with the best when multicollinearity level is high(λ>0.8 or λ-0.49).
文摘The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.
文摘The capital asset pricing model (CAPM) is a commonly used regression model in finance to model stock returns. Bayesian methods have been developed for the CAPM to account for market fluctuations within the industry. However, a Bayesian model checking procedure is needed to assess the CAPM in terms of the usual regression model assumptions of independence, homogeneity of variance, and normality. This paper develops Bayesian residuals and Bayesian p-values to check these model assumptions as well as to suggest model extensions to the CAPM.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
基金the National Natural Science Foundation of China under Grant Nos.10171094,10571001,and 30572285the Foundation of Nanjing Normal University under Grant No.2005101XGQ2B84+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No.07KJD110093the Foundation of Anhui University under Grant No.02203105
文摘在有固定设计的概括线性模型，在假设和另外的整齐条件下面，最大的伪可能性评估者的 asymptotic 规度，是有自然连接功能的伪可能性方程的根，被获得，在的地方表示最小的特征值， X <SUB > i </SUB >是围住的p ×& #8201 ； q 退回 ors ，和 y <SUB > i </SUB >是q ×& #8201 ； 1 回答。
基金Project supported by the National Natural Science Foundation of China.
文摘For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.
基金supported by the National Natural Science Foundation of China(Grant No.10471136)Ph.D.Program Foundation of Ministry of Education of China and Special Foundation of the Chinese Academy of Science and USTC.
文摘In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
基金Project supported by the National Natural Science Foundation of China and also supported by the U. S. Office of Naval Research and Air Force Office of Scientific Research.
文摘Consider the standard linear model where x<sub>x</sub>,x<sub>2</sub>… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e<sub>1</sub>, e<sub>2</sub>, …the independent random error sequence, each having a median zero. Define the minimum L<sub>1</sub>norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:
