Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models

Journal Article (Journal Article)

This work proposes new inference methods for a regression coefficient of interest in a (heterogenous) quantile regression model. We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a subset of them suffices to construct a reasonable approximation to the conditional quantile function. The proposed methods are (explicitly or implicitly) based on orthogonal score functions that protect against moderate model selection mistakes, which are often inevitable in the approximately sparse model considered in the present article. We establish the uniform validity of the proposed confidence regions for the quantile regression coefficient. Importantly, these methods directly apply to more than one variable and a continuum of quantile indices. In addition, the performance of the proposed methods is illustrated through Monte Carlo experiments and an empirical example, dealing with risk factors in childhood malnutrition. Supplementary materials for this article are available online.

Full Text

Duke Authors

Cited Authors

  • Belloni, A; Chernozhukov, V; Kato, K

Published Date

  • April 3, 2019

Published In

Volume / Issue

  • 114 / 526

Start / End Page

  • 749 - 758

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1080/01621459.2018.1442339

Citation Source

  • Scopus