Robust estimation of joint mean and scale covariance models with moving average Cholesky decomposition for longitudinal data

In this paper, we propose robust estimation of joint mean and scale covariance models for longitudinal data with multivariate power exponential distribution, which contains both leptokurtic and platykurtic distributions. Moreover, the moving average Cholesky decomposition is adopted to automatically guarantee the positive definiteness of the scale covariance matrix, which itself rather than its inverse matrix may be of mainly scientific interest. Since normal and Laplace distributions are special power exponential distributions, both of the corresponding joint models can be termed as special cases of the proposal. The iterative quasi-Fisher scoring algorithm is presented, strong consistency and asymptotic normality of the maximum likelihood estimators are proved, and the forward prediction method for the responses is developed. The simulation studies and real data analysis illustrate the effectiveness and robustness of the proposed joint model.