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Parsimonious Mean-Covariance Modeling for Longitudinal Data with ARMA Errors

Journal of Systems Science & Complexity 2019年第6期32卷 1675-1692页

作者： WANG Jiangli CHEN Yu ZHANG Weiping Department of Statistics and Finance University of Science and Technology of China

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 *** resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed under mild *** 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.

关键词： Autoregressive and moving average generalized estimating equation longitudinal data modified cholesky decomposition

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Efficient Estimation of Longitudinal Data Additive Varying Coefficient Regression Models

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 529-550页

作者： Shu LIU School of Statistics and Information Shanghai University of International Business and Economics Shanghai 201620 China School of Statistics and Management Shanghai University of Finance and Economics Shanghai 200433 China

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.

关键词： additive vary-coefficient model longitudinal data modified cholesky decomposition withinsubject correlation

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维普期刊数据库

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Joint semiparametric mean-covariance model in longitudinal study

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Science China Mathematics 2011年第1期54卷 145-164页

作者： MAO Jie ZHU ZhongYi Department of Statistics Fudan University Shanghai 200433 China

Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.

关键词： generalized estimating equation kernel estimation local linear regression modified cholesky decomposition semiparametric varying-coefficient partially linear model

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Estimation of Inverse Autocovariance Matrices for Long Memory Processes

Estimation of Inverse Autocovariance Matrices for Long Memor...

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第十届海峡两岸统计与概率研讨会

作者： C.-K.Ing H.-T.Chiou M.H.Guo “Academia Sinica” “National Sun Yat-sen University”

This work aims at estimating inverse autocovariance matrices of longmemory processes. A modified cholesky decomposition is used inconjunction with an increasing order autoregressive model to achievethis goal. The spectral norm consistency of the proposed estimate is established. We then extend this result to linear regression models withlong-memory time series errors. In particular, we show that when the objective is to consistently estimate the inverse autocovariance matrix of the error process, the same approach still works well if the estimated(by least squares) errors are used in place of the unobservable ones. Finally, a simulation study is performed to illustrate our theoretical findings.

关键词： inverse autocovariance matrix linear regression model long memory process modified cholesky decomposition

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