Encompassing Tests for Nonparametric Regressions

TL;DR

This paper develops fully nonparametric tests for model encompassing in nonparametric regressions, addressing bandwidth selection issues and validating a bootstrap method, with empirical evaluation demonstrating effectiveness in small samples.

Contribution

It introduces a novel framework for encompassing tests in nonparametric regressions and proposes new testing procedures that handle bandwidth selection and bootstrap validation.

Findings

Valid wild bootstrap method established

Effective small sample performance demonstrated

Two approaches for bias reduction in test statistics

Abstract

We set up a formal framework to characterize encompassing of nonparametric models through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for the encompassing hypothesis that are fully nonparametric. Our test statistics depend on kernel regression, raising the issue of bandwidth's choice. We investigate two alternative approaches to obtain a "small bias property" for our test statistics. We show the validity of a wild bootstrap method. We empirically study the use of a data-driven bandwidth and illustrate the attractive features of our tests for small and moderate samples.