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Roy’s largest root under rank-one perturbations: The complex valued case and applications

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  • Dharmawansa, Prathapasinghe
  • Nadler, Boaz
  • Shwartz, Ofer

Abstract

The largest eigenvalue of a single or a double Wishart matrix, both known as Roy’s largest root, plays an important role in a variety of applications. Recently, via a small noise perturbation approach with fixed dimension and degrees of freedom, Johnstone and Nadler derived simple yet accurate approximations to its distribution in the real valued case, under a rank-one alternative. In this paper, we extend their results to the complex valued case for five common single matrix and double matrix settings. In addition, we study the finite sample distribution of the leading eigenvector. We present the utility of our results in several signal detection and communication applications, and illustrate their accuracy via simulations.

Suggested Citation

  • Dharmawansa, Prathapasinghe & Nadler, Boaz & Shwartz, Ofer, 2019. "Roy’s largest root under rank-one perturbations: The complex valued case and applications," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:jmvana:v:174:y:2019:i:c:s0047259x18302896
    DOI: 10.1016/j.jmva.2019.05.009
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    References listed on IDEAS

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    1. I. M. Johnstone & B. Nadler, 2017. "Roy’s largest root test under rank-one alternatives," Biometrika, Biometrika Trust, vol. 104(1), pages 181-193.
    2. C. Khatri, 1969. "Non-central distributions ofith largest characteristic roots of three matrices concerning complex multivariate normal populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 23-32, December.
    3. Chiani, Marco, 2014. "Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy–Widom distribution," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 69-81.
    4. Chiani, Marco, 2016. "Distribution of the largest root of a matrix for Roy’s test in multivariate analysis of variance," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 467-471.
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    Cited by:

    1. Thu, Pham-Gia & Phong, Duong Thanh, 2022. "The distribution of the non-central Wilks statistic in the complex case," Statistics & Probability Letters, Elsevier, vol. 184(C).

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