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Encompassing Tests for Nonparametric Regressions

Author

Listed:
  • Elia Lapenta

    (CREST-THEMA - 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 - CNRS - Centre National de la Recherche Scientifique - THEMA - Théorie économique, modélisation et applications - CNRS - Centre National de la Recherche Scientifique - CY - CY Cergy Paris Université, IP Paris - Institut Polytechnique de Paris)

  • 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)

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.

Suggested Citation

  • Elia Lapenta & Pascal Lavergne, 2024. "Encompassing Tests for Nonparametric Regressions," Post-Print hal-04942518, HAL.
    • Handle: RePEc:hal:journl:hal-04942518
    DOI: 10.1017/S0266466624000100
    as

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