Uniform in bandwidth consistency of conditional U-statistics

摘要

In 1991 Stute introduced a class of estimators called conditionalU-statistics. They can be seen as a generalization of the Nadaraya-Watsonestimator, and their strong pointwise consistency to the general regressionfunction has been obtained in the same paper by Stute. Very recently, Gine andMason introduced the notion of a local U-process, which generalizes that of alocal empirical process, and obtained central limit theorems and laws of theiterated logarithm for this class. We apply the methods developed by Einmahland Mason (2005) and Gine and Mason (2007a,b) to establish uniform in bandwidthconsistency to the general regression function of the estimator proposed byStute.