Testing a Single Regression Coefficient in High Dimensional Regression Model

46 Pages Posted: 25 May 2016

See all articles by Wei Lan

Wei Lan

Peking University - Guanghua School of Management

Ping-Shou Zhong

Michigan State University

Runze Li

Pennsylvania State University

Hansheng Wang

Peking University - Guanghua School of Management

Chih-Ling Tsai

University of California, Davis - Graduate School of Management

Date Written: May 22, 2016

Abstract

In linear regression models with high dimensional data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable. This is mainly because the number of covariates exceeds the sample size. In this paper, we propose a simple and novel alternative by introducing the Correlated Predictors Screening (CPS) method to control for predictors that are highly correlated with the target covariate. Accordingly, the classical ordinary least squares approach can be employed to estimate the regression coefficient associated with the target covariate. In addition, we demonstrate that the resulting estimator is consistent and asymptotically normal even if the random errors are heteroscedastic. This enables us to apply the z-test to assess the significance of each covariate. Based on the p-value obtained from testing the significance of each covariate, we further conduct multiple hypothesis testing by controlling the false discovery rate at the nominal level. Then, we show that the multiple hypothesis testing achieves consistent model selection. Simulation studies and empirical examples are presented to illustrate the finite sample performance and the usefulness of the proposed method, respectively.

Keywords: Correlated Predictors Screening; False Discovery Rate; High Dimensional Data; Single Coefficient Test

JEL Classification: C30

Suggested Citation

Lan, Wei and Zhong, Ping-Shou and Li, Runze and Wang, Hansheng and Tsai, Chih-Ling, Testing a Single Regression Coefficient in High Dimensional Regression Model (May 22, 2016). Available at SSRN: https://ssrn.com/abstract=2783153 or http://dx.doi.org/10.2139/ssrn.2783153

Wei Lan (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

Ping-Shou Zhong

Michigan State University ( email )

Agriculture Hall
East Lansing, MI 48824-1122
United States

Runze Li

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

Hansheng Wang

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Chih-Ling Tsai

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States

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