Based on the generalized estimating equation approach,the authors propose a parsimonious mean-covariance model for longitudinal data with autoregressive and moving average error process,which not only unites the exist...Based on the generalized estimating equation approach,the authors propose a parsimonious mean-covariance model for longitudinal data with autoregressive and moving average error process,which not only unites the existing autoregressive Cholesky factor model and moving average Cholesky factor model but also provides a wide variety of structures of covariance matrix.The resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed under mild conditions.The authors demonstrate the effectiveness,parsimoniousness and desirable performance of the proposed approach by analyzing the CD4-I-cell counts data set and conducting extensive simulations.展开更多
We consider a longitudinal data additive varying coefficient regression model, in which the coef- ficients of some factors （covariates） are additive functions of other factors, so that the interactions between diffe...We consider a longitudinal data additive varying coefficient regression model, in which the coef- ficients of some factors （covariates） are additive functions of other factors, so that the interactions between different factors can be taken into account effectively. By considering within-subject correlation among repeated measurements over time and additive structure, we propose a feasible weighted two-stage local quasi-likelihood estimation. In the first stage, we construct initial estimators of the additive component functions by B-spline se- ries approximation. With the initial estimators, we transform the additive varying coefficients regression model into a varying coefficients regression model and further apply the local weighted quasi-likelihood method to estimate the varying coefficient functions in the second stage. The resulting second stage estimators are com- putationally expedient and intuitively appealing. They also have the advantages of higher asymptotic efficiency than those neglecting the correlation structure, and an oracle property in the sense that the asymptotic property of each additive component is the same as if the other components were known with certainty. Simulation studies are conducted to demonstrate finite sample behaviors of the proposed estimators, and a real data example is given to illustrate the usefulness of the proposed methodology.展开更多
基金supported by the National Key Research and Development Plan under Grant No.2016YFC0800100the National Science Foundation of China under Grant Nos.11671374,71771203,71631006
文摘Based on the generalized estimating equation approach,the authors propose a parsimonious mean-covariance model for longitudinal data with autoregressive and moving average error process,which not only unites the existing autoregressive Cholesky factor model and moving average Cholesky factor model but also provides a wide variety of structures of covariance matrix.The resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed under mild conditions.The authors demonstrate the effectiveness,parsimoniousness and desirable performance of the proposed approach by analyzing the CD4-I-cell counts data set and conducting extensive simulations.
基金Supported by Shanghai University of Finance and Economics Graduate Innovation and Creativity Funds(No.CXJJ-2013-458)
文摘We consider a longitudinal data additive varying coefficient regression model, in which the coef- ficients of some factors （covariates） are additive functions of other factors, so that the interactions between different factors can be taken into account effectively. By considering within-subject correlation among repeated measurements over time and additive structure, we propose a feasible weighted two-stage local quasi-likelihood estimation. In the first stage, we construct initial estimators of the additive component functions by B-spline se- ries approximation. With the initial estimators, we transform the additive varying coefficients regression model into a varying coefficients regression model and further apply the local weighted quasi-likelihood method to estimate the varying coefficient functions in the second stage. The resulting second stage estimators are com- putationally expedient and intuitively appealing. They also have the advantages of higher asymptotic efficiency than those neglecting the correlation structure, and an oracle property in the sense that the asymptotic property of each additive component is the same as if the other components were known with certainty. Simulation studies are conducted to demonstrate finite sample behaviors of the proposed estimators, and a real data example is given to illustrate the usefulness of the proposed methodology.
