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Since Robbins (1956), a large literature has evolved treating the empirical Bayes formulation of a sequence of decision problems. In this paper we look at the formulation and the asymptotic optimality criterion as a classical iid problem and a consistency property. With this point of view and the finite state component problem, we evoke classical results on Bayes procedures to prove a complete class theorem and to establish the asymptotic optimality of Bayes empirical Bayes…

通过最小分量识别有序二元正态分布AI 解读

For full-rank covariance matrix and other subfamilies of the ordered bivariate normal distribution, the identifiability of parameters by the minimum variate is demonstrated. For the general family, the distribution is not identified. These identifiability questions arise in connection with estimation within certain econometric models, for example, Tobin and Fair-Jaffee.

通过最小值变量识别有序二元正态分布AI 解读

For full-rank covariance matrix and other subfamilies of the ordered bivariate normal distribution, the identifiability of parameters by the minimum variate is demonstrated. For the general family, the distribution is not identified. These identifiability questions arise in connection with estimation within certain econometric models, for example, Tobin and Fair-Jaffee.

单调似然比族中经验贝叶斯单调多重决策问题的改进收敛率AI 解读

In the context of the two-action, linear loss, exponential family multiple decision problem, Van Houwelingen (1973), (1976) has shown that faster rates of convergence are deducible for monotone empirical Bayes procedures than result from application of the bound established for general empirical Bayes procedures by Johns and Van Ryzin (1972). This note generalizes a (1973) Van Houwelingen bound to arbitrary $k$-action, monotone loss, MLR family multiple decision problems. An…

两状态分量复合决策问题的渐近解：贝叶斯方法与比例参数的弥散先验AI 解读

Gilliland and Hannan (1974, Section 3) consider a general finite state compact risk component and reduce the problem of treating the asymptotic excess compound risk of Bayes compound rules to the question of $L_1$ consistency of certain induced estimators. This present paper considers the two state case and for several classes of diffuse symmetric priors on proportions establishes the $L_1$ consistency with rate. The rate $O(n^{-\frac{1}{2}})$ uniform in state sequences is…