Encompassing Tests for Nonparametric Regressions

Elia Lapenta and Pascal Lavergne
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Elia Lapenta: IP Paris - Institut Polytechnique de Paris, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Pascal Lavergne: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: We set up a formal framework to characterize encompassing of nonparametric models through the 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.

Date: 2024
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Published in Econometric Theory, 2024, pp.1-30. ⟨10.1017/S0266466624000100⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04942518

DOI: 10.1017/S0266466624000100

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