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Activity Number:
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520
- New Quantile-Modeling Methods for Large-Scale Heterogeneous Data
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Type:
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Invited
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Date/Time:
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Thursday, August 6, 2020 : 1:00 PM to 2:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #309429
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Title:
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Lean-Assumption Quantile Regression for High-Dimensional Data
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Author(s):
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Lan Wang*
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Companies:
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University of Minnesota
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Keywords:
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quantile regression; high dimension; minimax; L1 penalty; nonconvex penalty
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Abstract:
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$L_1$-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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Authors who are presenting talks have a * after their name.
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