Roy’s largest root test under rank-one alternatives

I. M. Johnstone and B. Nadler

Biometrika, 2017, vol. 104, issue 1, 181-193

Abstract: SUMMARY 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 $\chi^2$ and $F$. 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.

Keywords: Canonical correlation; Concentrated noncentrality; Greatest root statistic; Matrix perturbation; Multivariate analysis of variance; Roy’s largest root test. (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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