Encompassing Tests for Nonparametric Regressions

Abstract

We set up a formal framework to characterize encompassing of nonparametric mod-els through the L2 distance. We contrast it to previous literature on the comparison of nonparametric regression models. We then develop testing procedures for the encom-passing hypothesis that are fully nonparametric. Our test statistics depend on kernel regression, raising the issue of bandwidth’s choice. We investigate two alternative ap-proaches to obtain a “small bias property” for our test statistics. We show the validity of a wild bootstrap method, and we illustrate the attractive features of our tests for small and moderate samples.

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Replaced by

Elia Lapenta, and Pascal Lavergne, “Encompassing Tests for Nonparametric Regressions”, Econometric Theory, 2024, pp. 1–30, forthcoming.

Reference

Elia Lapenta, and Pascal Lavergne, “Encompassing Tests for Nonparametric Regressions”, TSE Working Paper, n. 22-1332, May 2022.