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A high-dimensional test on linear hypothesis of means under a low-dimensional factor model

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Abstract

In this paper, the problem of testing the hypothesis of linear combination of k-sample means of high-dimensional data is investigated under a low-dimensional factor model. We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of independent chi-squared distribution of 1 degree of freedom under the null hypothesis and mild conditions. We provide numerical studies on both sizes and powers to illustrate performance of the proposed test.

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Acknowledgements

The authors thank the Editor-in-Chief, Professor Maria Kateri, an associated editor and two anonymous referees for their constructive comments, suggestions and detailed advice that vastly improved this article. We also express our thanks to JEO assistant, Ms. Sangamithrai for her help in the process of revision of our paper. Cao’s research is supported by the National Statistical Science Research Program (No. 2020LY002), the National Natural Science Foundation of China (Nos. 11601008, 11526070) and Doctor Startup Foundation of Anhui Normal University (No. 2016XJJ101).

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Authors and Affiliations

  1. Department of Statistics, Anhui Normal University, Wuhu, 241000, China

    Mingxiang Cao

  2. School of Finance and Economics, Anhui Technical College of Industry and Economy, Hefei, 230051, China

    Yuanjing He

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  1. Mingxiang Cao
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  2. Yuanjing He
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Correspondence to Mingxiang Cao.

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Cao, M., He, Y. A high-dimensional test on linear hypothesis of means under a low-dimensional factor model. Metrika 85, 557–572 (2022). https://doi.org/10.1007/s00184-021-00841-2

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  • DOI: https://doi.org/10.1007/s00184-021-00841-2

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