New local estimation procedure for a non-parametric regression function for longitudinal data

The paper develops a new estimation of non-parametric 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 estimator proposed 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 procedure proposed, and to compare the procedure with the existing procedures. On the basis of our empirical studies, the newly proposed procedure works better than naive local linear regression with working independence error structure and the gain in efficiency can be achieved in moderate-sized samples. Our numerical comparison also shows that the newly proposed procedure outperforms some existing procedures. A real data set application is also provided to illustrate the estimation procedure proposed.