Encompassing Tests for Nonparametric Regressions

Résumé

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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Référence

Elia Lapenta et Pascal Lavergne, « Encompassing Tests for Nonparametric Regressions », TSE Working Paper, n° 22-1332, mai 2022.