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利用递减密度极大似然估计的均匀分布单调经验贝叶斯检验AI 解读

An empirical Bayes test for testing $\vartheta \leq \vartheta_0$ against $\vartheta > \vartheta_0$ for the uniform distribution on $\lbrack 0, \vartheta)$ is discussed. The relation is shown with the estimation of a decreasing density on $\lbrack 0, \infty)$ and a monotone empirical Bayes test is derived based on the least-concave majorant of the empirical distribution function. The asymptotic distribution of the Bayes risk is obtained and some Monte Carlo results are given.

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连续单参数指数族的单调经验贝叶斯检验AI 解读

Let $\theta$ be the natural parameter of a continuous one-parameter exponential family. An empirical Bayes test is constructed for testing $\theta \leqq 0$ against $\theta > 0$ with a piecewise linear loss function. Since the problem is monotone, Bayes tests for a given prior distribution can be characterized by a single parameter, e.g., the size of the test under $\theta = 0$. Therefore the construction of an empirical Bayes test can be reduced to the construction of an…