Testing Covariates in High Dimensional Regression

34 Pages Posted: 5 May 2013

See all articles by Wei Lan

Wei Lan

Peking University - Guanghua School of Management

Hansheng Wang

Peking University - Guanghua School of Management

Chih-Ling Tsai

University of California, Davis - Graduate School of Management

Date Written: May 3, 2013

Abstract

In a high dimensional linear regression model, we propose a new procedure for testing statistical significance of a subset of regression coefficients. Specifically, we employ the partial covariances between the response variable and the tested covariates to obtain a test statistic. The resulting test is applicable even if the predictor dimension is much larger than the sample size. Under the null hypothesis, together with boundedness and moment conditions on the predictors, we show that the proposed test statistic is asymptotically standard normal, which is further supported by Monte Carlo experiments. A similar test can be extended to generalized linear models. The practical usefulness of the test is illustrated via an empirical example on paid search advertising.

Keywords: Generalized Linear Model, High Dimensional Data, Hypotheses Testing, Paid Search Advertising, Partial Covariance, Partial F-Test

JEL Classification: C12, C13, C10

Suggested Citation

Lan, Wei and Wang, Hansheng and Tsai, Chih-Ling, Testing Covariates in High Dimensional Regression (May 3, 2013). Available at SSRN: https://ssrn.com/abstract=2260820 or http://dx.doi.org/10.2139/ssrn.2260820

Wei Lan

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

Hansheng Wang (Contact Author)

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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