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ENCOMPASSING TESTS FOR NONPARAMETRIC REGRESSIONS

Published online by Cambridge University Press:  17 April 2024

Elia Lapenta  and
Pascal Lavergne Open the ORCID record for Pascal Lavergne [Opens in a new window]
Elia Lapenta*
Affiliation:
CREST and ENSAE, Institut Polytechnique de Paris
Pascal Lavergne
Affiliation:
Toulouse School of Economics, Université Toulouse Capitole
*
Address correspondence to Elia Lapenta, CREST, 5 Avenue Le Chatelier, 91120 Palaiseau, France; e-mail: elia.lapenta@ensae.fr.
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Abstract

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We set up a formal framework to characterize encompassing of nonparametric models through the $L^2$ 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.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 30
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We thank the co-editor Michael Jansson and two referees for their comments that helped to improve the paper significantly. Elia Lapenta acknowledges funding from the French National Research Agency (ANR) under grant ANR-23-CE26-0008-01. Pascal Lavergne acknowledges funding from ANR under grant ANR-17-EURE-0010 (Investissements d’Avenir program).

References

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