Robust semiparametric modeling of mean and covariance in longitudinal data

Longitudinal data often suffer from heavy-tailed errors and outliers, which can significantly reduce efficiency and lead to invalid inferences. Robust techniques are essential, especially in joint mean-covariance modeling, as the estimation of the covariance matrix is more sensitive to heavy-tailed errors and outliers than the estimation of the mean. Motivated by the modified Cholesky decomposition of the covariance matrix, we propose a novel semiparametric method that uses robust techniques to simultaneously estimate the mean, autoregressive coefficients, and innovation variance. We provide a practical algorithm for this method and investigate the asymptotic properties of the mean and covariance estimators. Numerical simulations demonstrate that the proposed method is efficient and stable when the dataset is contaminated with outliers and heavy-tailed errors. The new robust technique yields statistically interpretable inferences in real data analysis, whereas traditional approaches fail to provide any acceptable inferences.