Random Quotients and the Behrens-Fisher Problem
Random Quotients and the Behrens-Fisher Problem
Let $\mathscr{P}_n$ be the space of $n \times n$ positive definite symmetric matrices. If $S_1$ and $S_2$ are random matrices in $\mathscr{P}_n, S_1$ is a better $\alpha$ denominator than $S_2$ (written $S_1 \prec_{(\alpha)} S_2$) $\operatorname{iff} U(x'S_1^{-1}x)^{\alpha/2} \ll_{st} U(x'S_2^{-1}x)^{\alpha/2}$ for all $x \in R^n$ where $U$ is uniform on [0, 1], …