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Abstract Details
Activity Number:
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152
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Type:
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Invited
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Date/Time:
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Monday, August 1, 2011 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract - #300118 |
Title:
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Sparse Quantile Regression Approach for Analyzing Heterogeneity in Ultrahigh-Dimension
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Author(s):
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Runze Li*+ and Lan Wang and Yichao Wu
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Companies:
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Penn State University and University of Minnesota and North Carolina State University
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Address:
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Department of Statistics, University Park, PA, 16802-2111,
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Keywords:
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Quantile Regression ;
SCAD ;
Ultrahigh-dimensional data
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Abstract:
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Ultrahigh-dimensional data is often heterogeneous due to either heteroscedastic variance or other forms of non-location-shift covariate effects. Quantile regression is particularly useful for analyzing data from heterogeneous population. Usually in practice, only a few covariates influence the conditional distribution of the response variable given all candidate covariates. We propose to systematically study sparse quantile regression for ultrahigh-dimensional data. For both computation and theoretic development, it is challenging to deal with both the nonsmooth loss function and the nonconvex penalty function in ultrahigh-dimensional parameter space. We develop a new algorithm to deal with computational issue and theoretically analyze the proposed algorithm. The new algorithm enables us to establish a new formulation of the oracle property for ultrahigh-dimensional data. We further study the sampling properties of the penalized quantile regression for ultrahigh-dimensional data under some regularity conditions which are weaker and more reasonable conditions than the existing ones in the literature.
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