Local Estimation For Semivarying Coefficient Model For Longitudinal Data

Longitudinal data refers to data of individuals observed repeatedly over time, which is widely used in practice. However, it usually cannot be well analyzed by traditional regression approaches for its feature of independence between groups and correlation in groups. In recent years, methods for many longitudinal data models such as single-variate nonparametric model, single-index model, partially linear model have been proposed. In this article we focus on semivarying coefficient model for longitudinal data. Based on Cholesky decomposition and profile least square techniques, we obtain the estimation of coefficients and covariance matrix simultaneously. We further prove the asymptotic properties of these estimators. Also simulation is conducted, of which the result shows that our estimation is fairly effective.