Smoothed quantile regression with large-scale inference

Xuming He, Xiaoou Pan, Kean Ming Tan and Wen-Xin Zhou

Journal of Econometrics, 2023, vol. 232, issue 2, 367-388

Abstract: Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. This paper focuses on statistical inference for quantile regression in the “increasing dimension” regime. We provide a comprehensive analysis of a convolution smoothed approach that achieves adequate approximation to computation and inference for quantile regression. This method, which we refer to as conquer, turns the non-differentiable check function into a twice-differentiable, convex and locally strongly convex surrogate, which admits fast and scalable gradient-based algorithms to perform optimization, and multiplier bootstrap for statistical inference. Theoretically, we establish explicit non-asymptotic bounds on estimation and Bahadur–Kiefer linearization errors, from which we show that the asymptotic normality of the conquer estimator holds under a weaker requirement on dimensionality than needed for conventional quantile regression. The validity of multiplier bootstrap is also provided. Numerical studies confirm conquer as a practical and reliable approach to large-scale inference for quantile regression. Software implementing the methodology is available in the R package conquer.

Keywords: Bahadur–Kiefer representation; Convolution; Quantile regression; Multiplier bootstrap; Non-asymptotic statistics (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407621001950
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:232:y:2023:i:2:p:367-388

DOI: 10.1016/j.jeconom.2021.07.010

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().