Testing a single regression coefficient in high dimensional linear models

Wei Lan, Ping Shou Zhong, Runze Li, Hansheng Wang, Chih Ling Tsai

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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data, the classical z-test (or t-test) for testing the significance of each single regression coefficient is no longer applicable.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.

Original languageEnglish (US)
Pages (from-to)154-168
Number of pages15
JournalJournal of Econometrics
Issue number1
StatePublished - Nov 1 2016

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Economics and Econometrics


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