Nonparametric Estimation Of A Smooth Regression Function Defined On A Domain Of Irk Irk PDF Download

The purpose of the paper is to develop methods for estimating regression functions (i.e., conditional expectations) when nothing is known or assumed about their underlying functional form. The approach is 'non-parametric' in the sense that the regression function itself, rather than a set of numerical parameters, is estimated. The methods given make use of certain rank order statistics and thereby avoid problems of scaling which are troublesome when less sophisticated non-parametric methods are used. The large sample performance of the proposed regression estimators is studied in detail and methods for obtaining high orders of asymptotic efficiency are given. The asymptotic (normal) distribution of the estimates is obtained and the related problem of prediction is discussed. (Author).