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连续单参数指数族经验贝叶斯检验的最优收敛率AI 解读

The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied. Previous results on this problem construct empirical Bayes tests via kernel density estimates. They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density estimates are useful.…

带序贯组成问题的经验贝叶斯检验AI 解读

We study the empirical Bayes decision theory with an $m$-truncated sequential statistical decision problem as the component. An empirical Bayes sequential decision procedure is constructed for the linear loss two-action problem. Asymptotic results are presented regarding the convergence of the Bayes risk of the empirical Bayes sequential decision procedure. With sequential components, an empirical Bayes sequential decision procedure selects both a stopping rule function and…