Asymptotically minimax Bayes predictive densities
Asymptotically minimax Bayes predictive densities
复制标题
渐进极小极大贝叶斯预测密度
DOI：
10.1214/009053606000000885
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发表时间：
2006
影响因子：
4.5
通讯作者：
M. Aslan
中科院分区：
文献类型：
--
作者：
M. Aslan
给定来自密度函数依赖于未知参数0的分布的随机样本，我们感兴趣的是在同一分布的未来观测中准确估计真实的参数密度函数。利用具有Kullback-Leibler损失函数D(f θ∥f) = f f θ log （f θ /f）的Bayes预测密度估计的渐近风险来检验选择先验分布的各种方法；研究的主要选择类型是极大极小。我们寻求相应的渐近风险为极大极小的渐近最不利预测密度。在多元位置家族的情况下，用最大似然估计正态均值的结果类似于Stein悖论：当模型的维数至少为3时，Jeffreys先验是极小极大的，尽管是不可接受的。对于一维和二维定位问题，Jeffreys先验既是可容许的，又是极大极小的。
Given a random sample from a distribution with density function that depends on an unknown parameter 0, 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 θ ∥f) = f f θ log (f θ /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 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.