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A new test for part of high dimensional regression coefficients

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  • Wang, Siyang
  • Cui, Hengjian

Abstract

It is well known that the F-test breaks down completely when the dimension of covariates exceeds the sample size. This paper proposes a new test for part of regression coefficients in high dimensional linear models. Under the high dimensional null hypothesis and various scenarios of the alternative, we derive the asymptotic distribution of the proposed test statistic, which allows power evaluation of the test. Through simulation studies, we demonstrate good finite-sample performance of the proposed test in comparison with the existing methods. The practical utility of our method is illustrated by a real data example.

Suggested Citation

  • Wang, Siyang & Cui, Hengjian, 2015. "A new test for part of high dimensional regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 187-203.
    • Handle: RePEc:eee:jmvana:v:137:y:2015:i:c:p:187-203
    DOI: 10.1016/j.jmva.2015.02.014
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    References listed on IDEAS

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    7. Wang, Siyang & Cui, Hengjian, 2013. "Generalized F test for high dimensional linear regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 134-149.
    8. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
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    Cited by:

    1. Rui Wang & Xingzhong Xu, 2021. "A Bayesian-motivated test for high-dimensional linear regression models with fixed design matrix," Statistical Papers, Springer, vol. 62(4), pages 1821-1852, August.

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