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INFERENCE IN NONPARAMETRIC SERIES ESTIMATION WITH SPECIFICATION SEARCHES FOR THE NUMBER OF SERIES TERMS

Published online by Cambridge University Press:  26 March 2020

Byunghoon Kang
Byunghoon Kang*
Affiliation:
Lancaster University
*
Address correspondence to Byunghoon Kang, Department of Economics, Lancaster University, Lancaster, United Kingdom; e-mail: b.kang1@lancaster.ac.uk; homepage: https://sites.google.com/site/davidbhkang.
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Abstract

Nonparametric series regression often involves specification search over the tuning parameter, that is, evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences for conditional mean functions in nonparametric series estimations that are uniform in the number of series terms. As a result, this paper constructs confidence intervals and confidence bands with possibly data-dependent series terms that have valid asymptotic coverage probabilities. This paper also considers a partially linear model setup and develops inference methods for the parametric part uniform in the number of series terms. The finite sample performance of the proposed methods is investigated in various simulation setups as well as in an illustrative example, that is, the nonparametric estimation of the wage elasticity of the expected labor supply from Blomquist and Newey (2002, Econometrica 70, 2455–2480).

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 2 , April 2021 , pp. 311 - 345
Copyright
© The Author(s), 2020. Published by Cambridge Univesity Press

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Footnotes

*

I thank the Editor Peter Phillips, the Co-Editor Iván Fernández-Val, and the two anonymous referees for thoughtful comments that significantly improved this paper. I am also grateful to Bruce Hansen, Jack Porter, Xiaoxia Shi, and Joachim Freyberger for useful comments and discussions, and thanks to Michal Kolesár, Denis Chetverikov, Yixiao Sun, Andres Santos, Patrik Guggenberger, Federico Bugni, Joris Pinkse, Liangjun Su, Myung Hwan Seo, and Áureo de Paula for helpful conversations and criticism. This paper is a revised version of the first chapter in my Ph.D. thesis at UW-Madison and previously titled “Inference in Nonparametric Series Estimation with Data-Dependent Undersmoothing.” I acknowledge support by the Kwanjeong Educational Foundation Graduate Research Fellowship and Leon Mears Dissertation Fellowship from UW-Madison. All errors are my own.

References

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