Kernel Regression Estimation Using Repeated Measurements Data

Abstract

Abstract The estimation of growth curves has been studied extensively in parametric situations. Here we consider the nonparametric estimation of an average growth curve. Suppose that there are observations from several experimental units, each following the regression model y(xi)=f(xj)+e(j=1,…,n), where e1, …, e n are correlated zero mean errors and 0≤x1<…<xn≤1 are fixed constants. We study some of the properties of a kernel estimator of f(x). Asymptotic and finite-sample results concerning the mean squared error of the estimator are obtained. In particular, the influence of correlation on the bandwidth minimizing mean squared error is discussed. A data-based method for selecting the bandwidth is illustrated in a data analysis. Most previous research on kernel regression estimators has involved uncorrelated errors. We investigate how dependence of the errors changes the behavior of a kernel estimator. Our theorems concerning the asymptotic mean squared error show that the estimator cannot be consistent un...