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Roy's largest root under rank-one perturbations: the complex valued case and applications.

Prathapasinghe Dharmawansa1, Boaz Nadler2, Ofer Shwartz2

  • 1Department of Electronic and Telecommunication Engineering, University of Moratuwa, Sri Lanka.

Journal of Multivariate Analysis
|September 3, 2019
PubMed
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This study extends approximations for Roy

Area of Science:

  • Statistics
  • Linear Algebra
  • Signal Processing

Background:

  • Roy's largest root, the largest eigenvalue of Wishart matrices, is crucial in various statistical applications.
  • Previous work by Johnstone and Nadler provided approximations for its distribution in the real-valued case under specific conditions.
  • The need for extensions to complex-valued scenarios and analysis of related eigenvector distributions was identified.

Purpose of the Study:

  • To extend the small noise perturbation approximations for Roy's largest root to complex-valued settings.
  • To analyze the finite sample distribution of the leading eigenvector associated with complex Wishart matrices.
  • To demonstrate the practical applications of these extended results in signal detection and communication systems.

Main Methods:

Keywords:
33C15Complex Wishart distributionRank-one perturbationRoy’s largest rootSeconday 62H10Signal detection in noise 2010 MSC: Primary 60B20

Related Experiment Videos

  • Application of small noise perturbation techniques to complex-valued single and double Wishart matrices.
  • Derivation of approximations for the distribution of Roy's largest root in five common settings.
  • Analysis of the leading eigenvector's distribution using similar perturbation methods.

Main Results:

  • Successfully extended Johnstone and Nadler's approximations to complex-valued cases for five matrix settings.
  • Derived novel results for the finite sample distribution of the leading eigenvector.
  • Validated the accuracy and utility of the derived approximations through simulations.

Conclusions:

  • The derived approximations offer accurate and computationally efficient tools for complex-valued statistical analysis.
  • The findings are directly applicable to enhancing performance in signal detection and communication systems.
  • This work provides a foundation for further research into high-dimensional matrix distributions and their applications.