Journal Article

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

Belloni, Alexandre, Kato, Kengo, Chernozhukov, Victor

2019

Overview

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.

• Publisher: Taylor & Francis,Taylor & Francis Group, LLC,Taylor & Francis Ltd
• Subject: Approximation / Childhood / Computer simulation / Confidence regions post-model selection / Economic models / Errors / Experiments / Inference / Malnutrition / Monte Carlo simulation / Orthogonal score functions / Quantile regression / Regression analysis / Regression coefficients / Regression models / risk / Risk analysis / Risk factors / sample size / Statistical methods / Statistics / Theory and Methods