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最大似然估计对任意有界碗形损失的二阶效率AI 解读

Let $X_1, X_2, \cdots$ be a sequence of i.i.d. random variables, each having density $f(x, \theta_0)$ where $\{f(x, \theta)\}$ is a family of densities with respect to a dominating measure $\mu$. Suppose $n^{\frac{1}{2}}(\hat{\theta} - \theta)$ and $n^{\frac{1}{2}}(T - \theta)$, where $\hat{\theta}$ is the mle and $T$ is any other efficient estimate, have Edgeworth expansions up to $o(n^{-1})$ uniformly in a compact neighbourhood of $\theta_0$. Then (under certain regularity…

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协方差矩阵完全可约时的均值向量并交检验AI 解读

The union-intersection test is derived for the mean vector of a multi-normal population when the covariance matrix is totally reducible. The performance of the test is compared to those of two other tests, the likelihood ratio test and a test discussed in Young (1976), using an information theory approach, by computing the small-sample powers through Monte Carlo techniques and also by computing the Pitman efficiency.