Exact Distribution of the Noncentral Complex Roy's Largest Root Statistic via Pieri's Formula
Statistics Theory
2025-07-30 v1 Statistics Theory
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).
Cite
@article{arxiv.2507.21508,
title = {Exact Distribution of the Noncentral Complex Roy's Largest Root Statistic via Pieri's Formula},
author = {Koki Shimizu and Hiroki Hashiguchi},
journal= {arXiv preprint arXiv:2507.21508},
year = {2025}
}