论文检索

多元线性假设检验的精确Bahadur效率AI 解读

The notion of Bahadur efficiency is used to compare multivariate linear hypothesis tests based on six criteria: (1) Roy's largest root, (2) the likelihood ratio test, (3) the Lawley-Hotelling trace, (4) Pillai's trace, (5) Wilks' $U$, and (6) Olson's statistic. Bahadur exact slope is computed for each statistic as a function of noncentrality parameters using results for probabilities of large deviations. The likelihood ratio test is shown to be asymptotically optimal in the…

多元正态分布似然比检验的渐近最优性AI 解读

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…