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Activity Number: 520 - New Quantile-Modeling Methods for Large-Scale Heterogeneous Data
Type: Invited
Date/Time: Thursday, August 6, 2020 : 1:00 PM to 2:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #309429
Title: Lean-Assumption Quantile Regression for High-Dimensional Data
Author(s): Lan Wang*
Companies: University of Minnesota
Keywords: quantile regression; high dimension; minimax; L1 penalty; nonconvex penalty
Abstract:

$L_1$-regularized quantile regression provides a fundamental technique for analyzing high-dimensional data that are heterogeneous with potentially heavy-tailed random errors. We show that $l_1$-QR can achieve the near-oracle error bound for estimating the regression coefficients under conditions weaker than those in the literature; and that $l_1$-QR is almost optimal in a minimax sense without requiring the Gaussian error assumption. We provide both theoretical and numerical evidence for scenarios where $l_1$-QR can outperform LS-Lasso. Furthermore, we show that under some regularity conditions, any local solution of nonconvex penalized quantile regression can achieve the near oracle rate in high dimension.


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