Considerations for the Linear Estimation of a Regression Function When the Data are Correlated.

A repeated-measurements model applicable in growth curve analysis, with correlated errors within subjects is developed. Kernel estimators of the population regression function are examined for various correlation functions. Limiting forms of an optimal linear combination of the subject means derived. Conditions for consistency of a general linear estimator are stated for the Ornstein-Uhlenbeck correlation function and a more general covariance structure. A numerical study investigating the requisite amount of smoothing and the efficiency of four popular kernel estimators is carried out. The expected values of the estimators are compared against one another and against an optimal linear combination. Keywords: Nonparametric regression; Growth curves; Correlated data; Optimum bandwidth; Mean averaged square error.