Distribution of the largest root of a matrix for Roy’s test in multivariate analysis of variance

详细信息    查看全文

• 作者：Marco Chiani ^{marco.chiani@unibo.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 62H10 ; secondary ; 62H15 ; 62J10
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：143
• 期：Complete
• 页码：467-471
• 全文大小：379 K

文摘

Let $X,Y$ denote two independent real Gaussian $p\times m$ and $p\times n$ matrices with $m,n\ge p$, each constituted by zero mean independent, identically distributed columns with common covariance. The Roy’s largest root criterion, used in multivariate analysis of variance (MANOVA), is based on the statistic of the largest eigenvalue, 717544cf4b0890a810dc60373ea">${\Theta }_1$, of ${(A+B)}^{-1}B$, where $A={\mathrm{XX}}^T$ and $B={\mathrm{Y\; Y}}^T$ are independent central Wishart matrices. We derive a new expression and efficient recursive formulas for the exact distribution of 717544cf4b0890a810dc60373ea">${\Theta }_1$. The expression can be easily calculated even for large parameters, eliminating the need of pre-calculated tables for the application of the Roy’s test.