ℓ[subscript 1]-penalized quantile regression in high-dimensional sparse models

By Alexandre Belloni, Victor Chernozhukov. 2011

210 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2e266fb44286844f171fb4788215a00ced8f3d13

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Citations in the corpus

High‐dimensional quantile regression: Convolution smoothing and concave regularization (2021, methodology): “The Lasso has the lowest SSE compared to QR-Lasso and SQR-Lasso, which coincides with the fact that QR does lose some efficiency in a normal model.”
Adaptive Huber Regression (2017, methodology): “The main focus of this paper is on the conditional mean regression in the presence of heavy-tailed noise, which automatically distinguishes our method from quantile-based robust regressions [Belloni and Chernozhukov (2011); Zheng, Peng and He (2015)].”
STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION (2012, methodology): “…(A4) and the assumption of Theorem 2 in Belloni and Chernozhukov (2011), which implies γ → 0, for any A > 1 and p −1 ≤ α → 0, if λ lasso satisfies (3.8) of Belloni and Chernozhukov (2011), with probability at least 1 – α – 4 γ − 3 p − A 2 , β̂ lasso satisfies where C 2 > 0 is a fixed…”
Supplementary Appendix for"Inference on Treatment Effects After Selection Amongst High-Dimensional Controls" (2013, unknown): “We shall invoke the following lemma derived in Belloni and Chernozhukov (2011).”
Uniform Inference for High-dimensional Quantile Regression: Linear Functionals and Regression Rank Scores (2017, methodology): “The lemma follows since n−1||Xδ||1 = n−1 ∣∣∣∣ ∣∣∣∣XS ( β̂o(τ)− β∗S(τ) ) ∣∣∣∣ ∣∣∣∣ 1 = OP ( s √ log(n) n ) for all τ ∈ [ , 1− ] by adapting the proof of Theorem 2 in Belloni and Chernozhukov (2011).”
Penalized expectile regression: an alternative to penalized quantile regression (2018, background): “Belloni and Chernozhukov (2011) study theory of quantile regression with lasso penalty in an ultra-high-dimensional setting, and Belloni et al.”
From Predictive to Prescriptive Analytics (2014, methodology): “1-regularized quantile regression of Belloni and Chernozhukov (2011).”