TITLE:
Joint Variable Selection of Mean-Covariance Model for Longitudinal Data
AUTHORS:
Dengke Xu, Zhongzhan Zhang, Liucang Wu
KEYWORDS:
Joint Mean and Covariance Models; Variable Selection; Cholesky Decomposition; Longitudinal Data; Penalized Maximum Likelihood Method
JOURNAL NAME:
Open Journal of Statistics,
Vol.3 No.1,
February
20,
2013
ABSTRACT: In this paper we reparameterize covariance structures in
longitudinal data analysis through the modified Cholesky decomposition of
itself. Based on this modified Cholesky decomposition, the within-subject
covariance matrix is decomposed into a unit lower triangular matrix involving
moving average coefficients and a diagonal matrix involving innovation variances,
which are modeled as linear functions of covariates. Then, we propose a
penalized maximum likelihood method for variable selection in joint
mean and covariance models based on this decomposition. Under certain regularity
conditions, we establish the consistency and asymptotic normality of the
penalized maximum likelihood estimators of parameters in the models. Simulation
studies are undertaken to assess the finite sample performance of the proposed
variable selection procedure.