Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function

TLDR

Longitudinal data analysis requires accurate covariance estimation for efficient regression and trajectory prediction, but irregular observation times make this challenging. The study proposes semiparametric covariance models that impose a parametric correlation structure with a nonparametric variance function, and introduces a varying‑coefficient partially linear model with a profile weighted least squares estimation procedure. A kernel estimator is used for the variance function, while quasi‑likelihood and minimum generalized variance methods estimate correlation parameters; the authors derive asymptotic properties, evaluate finite‑sample performance via simulations, and demonstrate the approach on real data.

Abstract

Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data. Both involve estimation of the covariance function. Yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed. A kernel estimator for estimating the nonparametric variance function is developed. Two methods for estimating parameters in the correlation structure—a quasi-likelihood approach and a minimum generalized variance method—are proposed. A semiparametric varying coefficient partially linear model for longitudinal data is introduced, and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed. Sampling properties of the proposed estimation procedures are studied, and asymptotic normality of the resulting estimators is established. Finite-sample performance of the proposed procedures is assessed by Monte Carlo simulation studies. The proposed methodology is illustrated with an analysis of a real data example.