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The likelihood ratio test for high-dimensional linear regression model

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  • Junshan Xie
  • Nannan Xiao

Abstract

The paper considers a significance test of regression variables in the high-dimensional linear regression model when the dimension of the regression variables p, together with the sample size n, tends to infinity. Under two sightly different cases, we proved that the likelihood ratio test statistic will converge in distribution to a Gaussian random variable, and the explicit expressions of the asymptotical mean and covariance are also obtained. The simulations demonstrate that our high-dimensional likelihood ratio test method outperforms those using the traditional methods in analyzing high-dimensional data.

Suggested Citation

  • Junshan Xie & Nannan Xiao, 2017. "The likelihood ratio test for high-dimensional linear regression model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8479-8492, September.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:17:p:8479-8492
    DOI: 10.1080/03610926.2016.1183785
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