Statistical Inference Of Mean-covariance Models For Multivariate Longitudinal Data

In this thesis, we mainly study the statistical inference of joint mean and covariance matrix model for multivariate longitudinal data. The thesis is divided into two parts. In the first part, we investigate the estimation of joint mean and covariance matrix model for multivariate longitudinal data. In order to deal with the high dimension and the positive definite constraint of covariance matrix, we develope a novel modified Cholesky block decomposition to parameterize covariance matrix itself, and the factor after decomposition have a moving average and log-innovation interpretation in time series. And after that we establish a time or time interval polynomial model. In this paper, the estimators of parameters by maximum likelihood estimator are obtained. The resulting estimators are shown to be consistent and asymptotic normality. A simulation study is conducted to illustrate the finite sample performance of the proposed decomposition method and compared with modified Cholesky block decomposition which was developed by Kim and Zimmerman(2012). In the second part, a variable selection for joint mean-covariance model is studied, based on BIC criteria. This paper develop a variable selection algorithm based on BIC criteria, for the asymptotic covariance matrix of the parameters is block diagonal matrix, which not only to select and estimate the important explanatory variables, but also easy to calculate. The variable selection algorithm is shown to be consistent. A simulation study is conducted to illustrate the finite sample performance of the proposed algorithm.There are two distinguished features in this thesis: Firstly, the joint mean and covariance matrix model under the one-dimensional longitudinal data is considered in many literatures currently. The statistical inference for multivariate longitudinal data has been an important aspect of statistical study, while relevant literatures not complete. This paper studies the statistical inference of this model under multivariate longitudinal data. Secondly, we not only consider the estimations and their asymptotic normality of the parameters under the joint mean-covariance model based on the novel modified Cholesky block decomposition, but also develop a variable select algorithm based on BIC criteria, which avoids a lot of calculation.