Numerical computation for the exact distribution of Roy’s largest root statistic under linear alternative
Numerical computation for the exact distribution of Roy’s largest root statistic under linear alternative
复制标题
DOI：
10.1007/s42081-022-00182-y
复制
发表时间：
2022-05
影响因子：
1.3
通讯作者：
Koki Shimizu;Hiroki Hashiguchi
中科院分区：
文献类型：
--
作者：
Koki Shimizu;Hiroki Hashiguchi
本文讨论了多元方差分析 (MANOVA) 中罗伊检验的精确功效的计算。我们根据区域多项式的乘积推导出奇异非中心 Beta 矩阵的最大特征值的精确表达式。该分布的数值计算是通过将区域多项式的乘积展开为区域多项式的线性组合的算法来进行的。此外，我们以一种便于线性替代方案下数值计算的形式提供了最大特征值的精确分布。
This paper discusses the computation of exact powers for Roy’s test in multivariate analysis of variance (MANOVA). We derive an exact expression for the largest eigenvalue of a singular noncentral Beta matrix in terms of the product of zonal polynomials. The numerical computation for that distribution is conducted by an algorithm that expands the product of zonal polynomials as a linear combination of zonal polynomials. Furthermore, we provide an exact distribution of the largest eigenvalue in a form that is convenient for numerical calculations under the linear alternative.