Testing Low-Dimensional Coefficients in High-Dimensional Heteroscedastic Linear Models

• Activity Number: 369
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• 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

Abstract

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.