Semiparametric Longitudinal Model with Irregular Time autoregressive error process

Abstract

This paper 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. The asymptotic bias and variance of the two stage local polynomial estimator are derived. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. A dataset of CD4 cell counts of HIV seroconverters is analyzed to demonstrate its application.