Working paper

Encompassing Tests for Nonparametric Regressions

Elia Lapenta, and Pascal Lavergne


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.


Encompassing; Nonparametric Regression; Bootstrap; Bias Correction; Locally Robust Statistic.;

JEL codes

  • C0: General
  • C12: Hypothesis Testing: General
  • C14: Semiparametric and Nonparametric Methods: General


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

See also

Published in

TSE Working Paper, n. 22-1332, May 2022