Abstract
In multivariate analysis under normality assumptions, many likelihood ratio criteria $(\lambda^{(n)})$ are distributed as $k\prod^m_{i=1} Z^a_{li}(1 - Z_{li})^{b_i}\prod^{m'}_{j=1} Z^{c_j}_{2j}$ for some constants, $k, m, m', a_i, b_i,$ and $c_j$ when their associated null hypotheses are true, where $Z_{ij}$ are independently distributed beta variates. Let $T^{(n)} = -n^{-1} \ln \lambda^{(n)}$. This paper shows that a sequence $\{T^{(n)}\}$ of this kind is asymptotically optimal in the sense of exact slopes. Explicit forms of the exact slopes are obtained.
Citation
H. K. Hsieh. "On Asymptotic Optimality of Likelihood Ratio Tests for Multivariate Normal Distributions." Ann. Statist. 7 (3) 592 - 598, May, 1979. https://doi.org/10.1214/aos/1176344680
Information