The Selection of Window Widths in Kernel Nonparametric Regression

Abstract

The estimation of the regression function using kernel density estimation techniques has long been hindered by reliance on subjective techniques for determining the window width required. Recent work in data-based optimal selection of nonparametric density estimates has eliminated the subjectivity of window selection for density estimation, but less attention has been given to the specialized nature of the kernel regression estimators. In this work, we demonstrate intuitively and empirically that a certain optimal bivariate window width is to be preferred over optimal univariate window widths in forming kernel estimators of r(x). Simulations also reveal how well data-based optimal kernel regression estimates perform for simple linear, polynomial, and exponential models.