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Limiting spectral distribution of high-dimensional noncentral Fisher matrices and its analysis

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Abstract

Fisher matrix is one of the most important statistics in multivariate statistical analysis. Its eigenvalues are of primary importance for many applications, such as testing the equality of mean vectors, testing the equality of covariance matrices and signal detection problems. In this paper, we establish the limiting spectral distribution of high-dimensional noncentral Fisher matrices and investigate its analytic behavior. In particular, we show the determination criterion for the support of the limiting spectral distribution of the noncentral Fisher matrices, which is the base of investigating the high-dimensional problems concerned with noncentral Fisher matrices.

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Acknowledgements

Zhidong Bai was supported by National Natural Science Foundation of China (Grant No. 12171198). Jiang Hu was supported by National Natural Science Foundation of China (Grant Nos. 12171078 and 11971097) and National Key R&D Program of China (Grant No. 2020YFA0714102). We thank the two reviewers for careful reading of the manuscript and their helpful comments that improve this paper.

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Authors and Affiliations

  1. Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Xiaozhuo Zhang, Zhidong Bai & Jiang Hu

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  1. Xiaozhuo Zhang
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  2. Zhidong Bai
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  3. Jiang Hu
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Correspondence to Jiang Hu.

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Zhang, X., Bai, Z. & Hu, J. Limiting spectral distribution of high-dimensional noncentral Fisher matrices and its analysis. Sci. China Math. 66, 393–408 (2023). https://doi.org/10.1007/s11425-020-1958-1

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  • DOI: https://doi.org/10.1007/s11425-020-1958-1

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