Estimating Explanatory Power in a Simple Regression Model Via Smoothers

摘要

Consider the regression model Y velence gamma(X) + epsilon, where gamma(X) is some conditional measure of location associated with Y, given X. Let Y be some estimate of Y, given X, and let (tau)~(2) (Y) be some measure of variation. Explanatory power is (eta)~(2) velence (tau)~(2)(Y)/(tau)~(2)(Y). When gamma(X) velence (beta)_(0) + (beta)_(1)X and (tau)~(2)(Y) is the variance of Y, (eta)~(2) velence (rho)~(2), where rho is Pearson's correlation. The small-sample properties of some methods for estimating a robust analog of explanatory power via smoothers is investigated. The robust version of a smoother proposed by Cleveland is found to be best in most cases.