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COMPLETE SUBSET AVERAGING FOR QUANTILE REGRESSIONS

Published online by Cambridge University Press:  13 August 2021

Ji Hyung Lee  and
Youngki Shin
Ji Hyung Lee
Affiliation:
University of Illinois
Youngki Shin
Affiliation:
McMaster University
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Abstract

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We propose a novel conditional quantile prediction method based on complete subset averaging (CSA) for quantile regressions. All models under consideration are potentially misspecified, and the dimension of regressors goes to infinity as the sample size increases. Since we average over the complete subsets, the number of models is much larger than the usual model averaging method which adopts sophisticated weighting schemes. We propose to use an equal weight but select the proper size of the complete subset based on the leave-one-out cross-validation method. Building upon the theory of Lu and Su (2015, Journal of Econometrics 188, 40–58), we investigate the large sample properties of CSA and show the asymptotic optimality in the sense of Li (1987, Annals of Statistics 15, 958–975) We check the finite sample performance via Monte Carlo simulations and empirical applications.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 1 , February 2023 , pp. 146 - 188
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

We would like to thank the Editor, Peter Phillips, the Co-Editor, Arthur Lewbel, and three anonymous referees for helpful comments and suggestions, which have led to substantial improvements. We would also like to thank Xun Lu and Liangjun Su for helpful discussion and sharing their codes. Shin is grateful for partial support by the Social Sciences and Humanities Research Council of Canada (SSHRC-435-2018-0275). This work was made possible by the facilities of WestGrid (www.westgrid.ca) and Compute Canada (www.computecanada.ca).

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