A new nested Cholesky decomposition and estimation for the covariance matrix of bivariate longitudinal data

In this paper, we propose a nested modified Cholesky decomposition for modeling the covariance structure in multivariate longitudinal data analysis. The entries of this decomposition have simple structures and can be interpreted as the generalized moving average coefficient matrices and innovation covariance matrices. We model the elements of these matrices by a class of unconstrained linear models, and develop a Fisher scoring algorithm to compute the maximum likelihood estimator of the regression parameters. The consistency and asymptotic normality of the estimators are established. Furthermore, we employ the smoothly clipped absolute deviation (SCAD) penalty to select the relevant variables in the models. The resulting SCAD estimators are shown to be asymptotically normal and have the oracle property. Some simulations are conducted to examine the finite sample performance of the proposed method. A real dataset is analyzed for illustration.