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Sign-based Test for Mean Vector in High-dimensional and Sparse Settings

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Abstract

In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Hu’nan University of Finance and Economics, Changsha, 410205, P. R. China

    Wei Liu

  2. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, P. R. China

    Ying Qiu Li

Authors
  1. Wei Liu
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  2. Ying Qiu Li
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Corresponding authors

Correspondence to Wei Liu or Ying Qiu Li.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant No. 11571052); Social Science Research Foundation of Hu’nan Provincial Department (Grant No. 15YBA066); Outstanding Youth Foundation of Hu’nan Provincial Department of Education (Grant No. 17B047)

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Liu, W., Li, Y.Q. Sign-based Test for Mean Vector in High-dimensional and Sparse Settings. Acta. Math. Sin.-English Ser. 36, 93–108 (2020). https://doi.org/10.1007/s10114-019-8290-z

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  • DOI: https://doi.org/10.1007/s10114-019-8290-z

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