Semiparametric Longitudinal Model with Irregular Time Autoregressive Error Process

This talk considers semiparametric inference for longitudinal data collected at irregular and possibly subject-specific times. We propose an irregular time autoregressive model for the error process in a partially linear model and develop a unified semiparametric profiling approach to estimating the regression parameters and autoregressive coefficients. An appealing feature of the proposed method is that it can effectively accommodate irregular and  subject-specific observation times.We establish the asymptotic normality of the proposed estimators and derive  explicit forms of their asymptotic variances. For the nonparametric component, we construct  a two stage local polynomial estimator. Our method takes into account the autoregressive error structure and does not drop any observations.