ИСТИНА

We consider famous MANOVA test statistics: the likelihood ratio test statistics $T_{LR}$, Lawley-Hotelling’s generalized statistics $T_{LH}$, and Bartlett-Nanda-Pillai’s test statistics $T_{BNP}$ when a number $n$ of observations is comparable with its dimension $p$, e.g. $p/n \rightarrow c \in (0, 1)$. Since the exact distributions of these statistics are complicated and not easy to treat, we need some approximations for them. The non-asymptotic results for $T_{LR}$ were obtained in 2006 in the Ulyanov, Wakaki and Fujikoshi paper. The talk is devoted to similar non-asymptotic bounds for distributions of $T_{LH}$ and $T_{BNP}$. The research was supported by RFBR grant, No. 14-01-00500, and by RSCF 14-11-00364.