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Encompassing Tests for Nonparametric Regressions

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  • Elia Lapenta
  • Pascal Lavergne

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.

Suggested Citation

  • Elia Lapenta & Pascal Lavergne, 2022. "Encompassing Tests for Nonparametric Regressions," Papers 2203.06685, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2203.06685
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    References listed on IDEAS

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