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多参数指数族中简单假设贝叶斯检验的渐近行为AI 解读

The asymptotic form of the Bayes acceptance region is derived for testing simple null-hypotheses in multiparameter exponential families. This result suggests a reasonable definition for tests which might be called "almost-Bayes". The rate at which the risk of the Bayes test converges to zero is obtained, showing the nature of its dependence on the prior distribution and providing a basis for comparison of almost-Bayes procedures. Concluding remarks contain a brief discussion…

贝叶斯检验与贝叶斯风险的渐近行为AI 解读

In this paper the asymptotic behaviors of the Bayes test and Bayes risk are studied in both the one-sided and two-sided testing problems, where the independent observations are taken from one member of a one-parameter exponential family. Precise asymptotic expressions are found which show the Bayes procedure to be relatively insensitive to the prior distribution as the sample size increases to infinity.

正态均值与方差线性函数的双侧置信区间札记AI 解读

The confidence sets for linear functions $\mu + \lambda\sigma^2$ of the mean $\mu$ and variance $\sigma^2$ of a normal distribution, defined in terms of the uniformly most powerful unbiased level $\alpha$ tests of hypotheses of form $H_0(\lambda, m): \mu + \lambda\sigma^2 = m$ against the two-sided alternative $H_1(\lambda, m): \mu + \lambda\sigma^2 \neq m$ for $-\infty < m < \infty$, for fixed $\alpha$ and $\lambda$, are shown to be intervals if the number of degrees of…