Relative error prediction via kernel regression smoothers

Abstract

In this article, we introduce and study local constant and local linear nonparametric regression estimators when it is appropriate to assess performance in terms of mean squared relative error of prediction. We give asymptotic results for both boundary and non-boundary cases. These are special cases of more general asymptotic results that we provide concerning the estimation of the ratio of conditional expectations of two functions of the response variable. We also provide a good bandwidth selection method for the estimators. Examples of application, limited simulation results and discussion of related problems and approaches are also given.