Details of Research Outputs

In this paper we propose a nonparametric data-driven approach to model covariance structures for longitudinal data. Based on a modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving generalized autoregressive coefficients and a diagonal matrix involving innovation variances. Local polynomial smoothing estimation is proposed to model the nonparametric smoothing functions of the mean, generalized autoregressive coefficients and (log) innovation variances, simultaneously. We provide theoretical justification of consistency of the fitted smoothing curves in the mean, generalized autoregressive parameters and (log) innovation variances. Two real data sets are analyzed for illustration. Simulation studies are made to evaluate the efficacy of the proposed method.