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

ABSTRACT: Roy's largest root is a common test statistic in multivariate analysis, statistical signal processing and allied fields. Despite its ubiquity, provision of accurate and tractable approximations to its distribution under the alternative has been a longstanding open problem. Assuming Gaussian observations and a rank-one alternative, or concentrated noncentrality, we derive simple yet accurate approximations for the most common low-dimensional settings. These include signal detection in noise, multiple response regression, multivariate analysis of variance and canonical correlation analysis. A small-noise perturbation approach, perhaps underused in statistics, leads to simple combinations of standard univariate distributions, such as central and noncentral [Formula: see text] and [Formula: see text]. Our results allow approximate power and sample size calculations for Roy's test for rank-one effects, which is precisely where it is most powerful.

SUBMITTER: Johnstone IM

PROVIDER: S-EPMC5793689 | biostudies-literature | 2017 Mar

REPOSITORIES: biostudies-literature

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

Johnstone I M IM Nadler B B

Biometrika 20170113 1

Roy's largest root is a common test statistic in multivariate analysis, statistical signal processing and allied fields. Despite its ubiquity, provision of accurate and tractable approximations to its distribution under the alternative has been a longstanding open problem. Assuming Gaussian observations and a rank-one alternative, or concentrated noncentrality, we derive simple yet accurate approximations for the most common low-dimensional settings. These include signal detection in noise, mult ...[more]

PMID: 29430030

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