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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | A. Belloni and V. Chernozhukov (2011) $_1$-penalized quantile regression for high dimensional sparse models | 1.000 | 7 | 3 | 100% |
| 2 | Roger Koenker (2005) Quantile Regression | 1.000 | 6 | 5 | 100% |
| 3 | A. Belloni, D. Chen, V. Chernozhukov, and C. Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.811 | 4 | 2 | 100% |
| 4 | A. Belloni, V. Chernozhukov, and C. Hansen (2014) Inference on treatment effects after selection amongst high-dimensional controls | 0.811 | 4 | 2 | 100% |
| 5 | K. Kato (2011) Group Lasso for high dimensional sparse quantile regression models | 0.811 | 4 | 2 | 100% |
| 6 | Hannes Leeb and Benedikt M. Pötscher (2005) Model selection and inference: facts and fiction | 0.737 | 3 | 2 | 100% |
| 7 | Victor Chernozhukov and Christian Hansen (2008) Instrumental variable quantile regression: A robust inference approach self | 0.737 | 3 | 2 | 100% |
| 8 | P. J. Bickel, Y. Ritov, and A. B. Tsybakov (2009) Simultaneous analysis of lasso and Dantzig selector | 0.644 | 4 | 1 | 100% |
| 9 | A. Belloni, V. Chernozhukov, and I. Fernandez-Val (2011) Conditional quantile processes based on series or many regressors | 0.644 | 2 | 2 | 100% |
| 10 | Victor H. de la Peña, Tze Leung Lai, and Qi-Man Shao (2009) Self-normalized Processes: Limit Theory and Statistical Applications | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 40 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | 2303.02784 | 1.000 | 5 | 3 |
| 2 | Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments | 0.511 | 2 | 1 |
| 3 | Conditional Quantile Processes based on Series or Many Regressors | 0.405 | 1 | 1 |
| 4 | On LASSO for Predictive Regression | 0.405 | 1 | 1 |
| 5 | Minimax Semiparametric Learning With Approximate Sparsity | 0.405 | 1 | 1 |
| 6 | Sparse Quantile Regression | 0.405 | 1 | 1 |
| 7 | 2506.22754 | 0.405 | 1 | 1 |