New Local Estimation Procedure for Nonparametric Regression Function of Longitudinal Data

This paper develops a new estimation of nonparametric regression functions for clustered or longitudinal data. We propose to use Cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously. We further prove that the proposed estimator is as asymptotically efficient as if the covariance matrix were known. A Monte Carlo simulation study is conducted to examine the finite sample performance of the proposed procedure, and to compare the proposed procedure with the existing ones. Based on our empirical studies, the newly proposed procedure works better than the naive local linear regression with working independence error structure and the efficiency gain can be achieved in moderate-sized samples. Our numerical comparison also shows that the newly proposed procedure outperforms some existing ones. A real data set application is also provided to illustrate the proposed estimation procedure.