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摘要翻译：
给定密度函数依赖于未知参数θ的分布的随机样本，我们感兴趣的是在未来的观测中从相同的分布精确估计真实的参数密度函数。用Kullback-Leibler损失函数$d(f_{\theta}{\hat{f}}）=\int{f_{\theta}\log{(f_{\theta}/hat{f}）}}$的Bayes预测密度估计的渐近风险研究了先验分布的各种选择方法；研究的主要选择类型是极小极大。我们寻求相应的渐近风险为极小极大的渐近最小有利预测密度。一个类似于Stein悖论的用极大似然估计正规均值的结果对于多元位置族情形中的一致先验成立：当模型的维数至少为3时，Jeffreys先验是极小极大的，尽管是不可容许的。对于一维和二维定位问题，Jeffreys先验既是容许的，又是极小极大的。
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英文标题：
《Asymptotically minimax Bayes predictive densities》
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作者：
Mihaela Aslan
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same distribution. The asymptotic risk of Bayes predictive density estimates with Kullback--Leibler loss function $D(f_{\theta}||{\hat{f}})=\int{f_{\theta} \log{(f_{\theta}/ hat{f})}}$ is used to examine various ways of choosing prior distributions; the principal type of choice studied is minimax. We seek asymptotically least favorable predictive densities for which the corresponding asymptotic risk is minimax. A result resembling Stein's paradox for estimating normal means by the maximum likelihood holds for the uniform prior in the multivariate location family case: when the dimensionality of the model is at least three, the Jeffreys prior is minimax, though inadmissible. The Jeffreys prior is both admissible and minimax for one- and two-dimensional location problems.
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PDF链接：
https://arxiv.org/pdf/708.0177
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