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

Alexandre Belloni, Victor Chernozhukov, Kengo Kato

arXiv 27 Dec 2013 · Mathematics — Statistics Theory · publishedJournal of the American Statistical Association (2018) · 53 citations (OpenAlex)

arXiv:1312.7186 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This work proposes new inference methods for a regression coefficient of interest in a (heterogeneous) quantile regression model. We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a subset of them suffice 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 paper. 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.

Citation extraction

40
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appendix boundary found by appendix_titled_section at “Proofs for Section \ref{Sec:Step1} of Supplementary Material” · 65% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1A. Belloni and V. Chernozhukov (2011) $_1$-penalized quantile regression for high dimensional sparse models1.00073100%
2Roger Koenker (2005) Quantile Regression1.00065100%
3A. Belloni, D. Chen, V. Chernozhukov, and C. Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain0.81142100%
4A. Belloni, V. Chernozhukov, and C. Hansen (2014) Inference on treatment effects after selection amongst high-dimensional controls0.81142100%
5K. Kato (2011) Group Lasso for high dimensional sparse quantile regression models0.81142100%
6Hannes Leeb and Benedikt M. Pötscher (2005) Model selection and inference: facts and fiction0.73732100%
7Victor Chernozhukov and Christian Hansen (2008) Instrumental variable quantile regression: A robust inference approach self0.73732100%
8P. J. Bickel, Y. Ritov, and A. B. Tsybakov (2009) Simultaneous analysis of lasso and Dantzig selector0.64441100%
9A. Belloni, V. Chernozhukov, and I. Fernandez-Val (2011) Conditional quantile processes based on series or many regressors0.64422100%
10Victor H. de la Peña, Tze Leung Lai, and Qi-Man Shao (2009) Self-normalized Processes: Limit Theory and Statistical Applications0.5112250%

Showing the top 10 of 40 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
12303.027841.00053
2Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments0.51121
3Conditional Quantile Processes based on Series or Many Regressors0.40511
4On LASSO for Predictive Regression0.40511
5Minimax Semiparametric Learning With Approximate Sparsity0.40511
6Sparse Quantile Regression0.40511
72506.227540.40511