标题： 先验的渐近可接受性与椭圆微分方程 显示英文标题

标题： Asymptotic admissibility of priors and elliptic differential equations

摘要： 我们通过相应估计量的二阶渐近行为来评估先验。在某些正则条件下，参数在域D（R^d的一个开连通子集）上取值的有效估计量之间的风险差异，渐近地表示为依赖于渐近协方差矩阵V的椭圆微分形式。 每个有效估计量具有与对应于先验密度p的“局部贝叶斯”估计量相同的渐近风险。估计量的渐近决策理论根据某些椭圆微分方程解的存在性，将光滑先验密度识别为可接受或不可接受。 如果在D的边界附近pV的值足够小，则先验p是可接受的。我们给出了当V=I,D=R^d-\{0)时唯一的可接受不变先验。 给出一个正态混合模型的详细示例。 显示英文摘要

摘要： We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.