Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models
By Alexandre Belloni, Victor Chernozhukov, Kengo Kato. Journal of the American Statistical Association, 2013
71 citations recorded by the source corpus.
ABSTRACT 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.
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/62f3678e60ef40d0c5ff7f2338c912af91a77f3c
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Citations in the corpus
- Uniform Inference for High-dimensional Quantile Regression: Linear Functionals and Regression Rank Scores (2017, methodology): “The latter can be treated as a condition on the initial step estimator – see Belloni et al. (2013) for more details where the authors introduce an additional step to remove this assumption.”
- Conditional quantile processes based on series or many regressors (2011, unknown): “is a challenging issue, since it needs to take into account the model selection mistakes in estimation, and is beyond the scope of the present paper; however, it is a subject of our ongoing research, see [10].”
- Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments (2019, unknown): “Alternative estimators for estimating the GPS can be the kernel density estimator, the artificial neural networks in Chen and White (1999), the Lasso methods in Su, Ura, and Zhang (2019), Belloni, Chernozhukov, and Kato (2019), Klosin (2021), 9 or the series cross-validated method in Zhang (2022).”