论文标题
在线性替代方面，Roy最大根统计的精确分布的数值计算
Numerical computation for the exact distribution of Roy's largest root statistic under linear alternative
论文作者
论文摘要
本文讨论了罗伊测试的确切功能在方差〜（Manova）中的测试计算。我们在Zonal多项式的乘积方面得出了奇异非中性β矩阵的最大特征值的精确表达。该分布的数值计算是通过一种算法进行的，该算法将纬向多项式的乘积扩展为纬向多项式的线性组合。此外，我们以一种方便的形式提供了最大的特征值的精确分布，该形式方便在线性替代方面进行数值计算。
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.
