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Activity Number: 369
Type: Contributed
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #320624
Title: Testing Low-Dimensional Coefficients in High-Dimensional Heteroscedastic Linear Models
Author(s): Honglang Wang* and Ping-Shou Zhong and Yuehua Cui
Companies: Indiana University Purdue University Indianapolis and Michigan State University and Michigan State University
Keywords: Empirical Likelihood ; Heteroscedasticity ; High Dimension

We consider hypothesis testing problems for a low-dimensional coefficient vector in a high-dimensional linear model with heteroscedastic variance. Heteroscedasticity is a commonly observed phenomenon in many applications including finance and genomic studies. Several statistical inference procedures have been proposed for low-dimensional coefficients in a high-dimensional linear model with homoscedastic variance. However, those procedures designed for homoscedastic variance are not applicable for models with heteroscedastic variance and the heteroscedasticity issue has not been investigated and studied. We propose a inference procedure based on empirical likelihood to overcome the heteroscedasticity issue. The proposed method is able to make valid inference under heteroscedasticity model even when the conditional variance of random error is a function of the high-dimensional predictor. We apply our inference procedure to three recently proposed estimating equations and establish the asymptotic distributions of the proposed methods. Some simulation studies and real data analyses are conducted to demonstrate the proposed methods.

Authors who are presenting talks have a * after their name.

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