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Exact Distribution of the Noncentral Complex Roy's Largest Root Statistic via Pieri's Formula
Koki Shimizu, Hiroki Hashiguchi · 2025-07-29 · via math.ST updates on arXiv.org

In this study, we derive the exact distribution and moment of the noncentral complex Roy's largest root statistic, expressed as a product of complex zonal polynomials. We show that the linearization coefficients arising from the product of complex zonal polynomials in the distribution of Roy's test under a specific alternative hypothesis can be explicitly computed using Pieri's formula, a well-known result in combinatorics. These results were then applied to compute the power of tests in the complex multivariate analysis of variance (MANOVA).

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