Joint estimation for single index mean—covariance models with longitudinal data

In this paper, based on the Cholesky decomposition, we construct a single index mean—covariance model for longitudinal data, and then propose a two-step estimation procedure. In the first step, we obtain initial estimators of index coefficient and the link function by ignoring the possible correlation between repeated measures. Then, generalized autoregressive coefficients and innovation variances are estimated based on these initial estimators. In the second step, we employ profile weighted least squares techniques to obtain the more efficient estimators of index coefficients and the unknown link function. All resulting estimators in both the mean and covariance models are shown to be consistent and asymptotically normal. Simulation study and a real data analysis show that the proposed estimators in this paper are more efficient than some existing approaches.