{"ID":2889052,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.21508","arxiv_id":"2507.21508","title":"Exact Distribution of the Noncentral Complex Roy's Largest Root Statistic via Pieri's Formula","abstract":"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).","short_abstract":"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 alt...","url_abs":"https://arxiv.org/abs/2507.21508","url_pdf":"https://arxiv.org/pdf/2507.21508v1","authors":"[\"Koki Shimizu\",\"Hiroki Hashiguchi\"]","published":"2025-07-29T05:19:24Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}