Subject-wise empirical likelihood inference for robust joint mean-covariance model with longitudinal data

In longitudinal studies, one of the biggest challenges is how to obtain a good estimator of covariance matrix to improve the estimation efficiency of the mean regression coefficients. Meanwhile, one outlier in a subject level may generate multiple outliers in the sample due to repeated measurements. To solve these problems, this paper develops a robust joint mean-covariance model using the bounded exponential score function and modified Cholesky decomposition. The motivation for this new procedure is that it enables us to achieve high effectiveness and robustness simultaneously by introducing an additional tuning parameter gamma which can be automatically selected using a data-driven procedure. In addition, we propose a subject-wise empirical likelihood to construct the confidence intervals/regions for the mean regression coefficients. Furthermore, under some mild conditions, we have established asymptotic theories of the proposed procedures. Finally, simulation studies are constructed to evaluate the finite sample performance of the proposed methods. A practical progesterone example is used to demonstrate the superiority of our proposed method.