Variable Selection in Robust Joint Mean and Covariance Model for Longitudinal Data Analysis

In longitudinal data analysis, a correct specification of the within-subject covariance matrix cultivates an efficient estimation for mean regression coefficients. In this article, we consider robust variable selection method in a joint mean and covariance model. We propose a set of penalized robust generalized estimating equations to simultaneously estimate the mean regression coefficients, the generalized autoregressive coefficients, and innovation variances introduced by the modified Cholesky decomposition. The set of estimating equations select important covariate variables in both mean and covariance models together with the estimating procedure. Under some regularity conditions, we develop the oracle property of the proposed robust variable selection method. Finally, a simulation study and a detailed data analysis are carried out to assess and illustrate the small sample performance; they show that the proposed method performs favorably by combining the robustifying and penalized estimating techniques together in the joint mean and covariance model.