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NONPARAMETRIC WEIGHTED AVERAGE QUANTILE DERIVATIVE

Published online by Cambridge University Press:  03 June 2021

Ying-Ying Lee
Ying-Ying Lee*
Affiliation:
University of California Irvine
*
Address correspondence to Ying-Ying Lee, Department of Economics, University of California Irvine, 3151 Social Science Plaza, Irvine, CA92697, USA; e-mail: [email protected].
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Abstract

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The weighted average quantile derivative (AQD) is the expected value of the partial derivative of the conditional quantile function (CQF) weighted by a function of the covariates. We consider two weighting functions: a known function chosen by researchers and the density function of the covariates that is parallel to the average mean derivative in Powell, Stock, and Stoker (1989, Econometrica 57, 1403–1430). The AQD summarizes the marginal response of the covariates on the CQF and defines a nonparametric quantile regression coefficient. In semiparametric single-index and partially linear models, the AQD identifies the coefficients up to scale. In nonparametric nonseparable structural models, the AQD conveys an average structural effect under certain independence assumptions. Including a stochastic trimming function, the proposed two-step estimator is root-n-consistent for the AQD defined by the entire support of the covariates. To facilitate tractable asymptotic analysis, a key preliminary result is a new Bahadur-type linear representation of the generalized inverse kernel-based CQF estimator uniformly over the covariates in an expanding compact set and over the quantile levels. The weak convergence to Gaussian processes applies to the differentiable nonlinear functionals of the quantile processes.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 3 , June 2022 , pp. 497 - 535
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 (http://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

This paper is based on the second chapter of my PhD dissertation. I am grateful to Bruce Hansen and Jack Porter for invaluable comments and guidance. I also thank Chris Tabor, Matias Cattaneo, David Jacho-Chávez, Alexandre Poirier, Emmanuel Guerre, Ingrid van Keilegom, and Efang Kong for helpful comments and discussion. Finally, I want to thank the Editor Peter C.B. Phillips, the Co-Editor Michael Jansson, and two anonymous referees whose comments have significantly improved this paper.

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