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Related Experiment Videos

Roy's largest root test under rank-one alternatives.

I M Johnstone1,2, B Nadler2

  • 1Department of Statistics, Sequoia Hall, 390 Serra Mall, Stanford University, California 94305, U.S.A.

Biometrika
|February 13, 2018
PubMed
Summary
This summary is machine-generated.

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Researchers developed accurate approximations for Roy

Area of Science:

  • Multivariate statistical analysis
  • Statistical signal processing

Background:

  • Roy's largest root is a widely used test statistic.
  • Accurate approximations for its distribution under the alternative are lacking.

Purpose of the Study:

  • To derive accurate and tractable approximations for Roy's largest root distribution.
  • To enable power and sample size calculations for rank-one effects.

Main Methods:

  • Assuming Gaussian observations and a rank-one alternative.
  • Utilizing a small-noise perturbation approach.
  • Deriving approximations using combinations of standard univariate distributions.

Main Results:

  • Simple and accurate approximations for common low-dimensional settings.
Keywords:
Canonical correlationConcentrated noncentralityGreatest root statisticMatrix perturbationMultivariate analysis of varianceRoy’s largest root test.

Related Experiment Videos

  • Applications in signal detection, regression, MANOVA, and canonical correlation.
  • Approximations involve central and noncentral t and F distributions.

    • Conclusions:

    • The derived approximations address a longstanding problem in multivariate statistics.
    • Enables practical power and sample size calculations for Roy's test.
    • The small-noise perturbation method offers a valuable statistical tool.