Empirical Bayes with a Changing Prior
研究了当先验分布随时间变化时，如何基于修正的经验密度估计构造决策规则，并证明了两类问题（二行动和估计问题）的渐近最优性及收敛速度。
We consider modified empirical Bayes problems in which the prior distribution of $\Theta$ at stage $n + 1$ is $G^{(n+1)}(\theta)$. The Bayes optimality criterion is now given by the sequence of functionals $R(G^{(n+1)}$. The observations $X_1, \cdots, X_n$ are no longer i.i.d so decision procedures are constructed based on modified empirical density estimates for $f_G^{(n+1)}(x)$. Asymptotic optimality together with asymptotic convergence rates is established for two action and estimation problems when the observations are drawn from a member of the one-parameter exponential family.