AI 中文总结
研究在平方误差损失下估计多元正态均值问题，通过引入新方法证明适当贝叶斯极小极大多重收缩估计量存在，其能自适应向更有前景目标收缩，解决多目标选择挑战，且构建方式与以往不同。
AI 中文摘要
对于在平方误差损失下估计多元正态均值的典型问题，我们首次通过引入一种显式构造的通用方法，证明了适当贝叶斯极小极大多重收缩估计量的存在性。与向单个预先指定目标收缩的极小极大收缩估计量不同，极小极大多重收缩估计量向一组预先指定目标中更有前景的目标自适应收缩，在保持至少与最大似然估计量一样好的保护的同时，大幅增加了潜在风险降低区域。这些估计量在实践中特别有用，因为当先验信息表明有多个可行的收缩目标可供选择时，它们解决了选择极小极大收缩估计量的挑战。与以前基于超调和边缘混合构建的形式贝叶斯极小极大多重收缩估计量不同，这些适当贝叶斯极小极大多重收缩估计量是通过平方根超调和边缘混合获得的。此类适当贝叶斯极小极大多重收缩估计量的示例包括经典斯特罗德曼收缩估计量的自适应凸组合。
英文摘要
For the canonical problem of estimating a multivariate normal mean under squared error loss, we demonstrate, for the first time, the existence of proper Bayes minimax multiple shrinkage estimators by introducing a general approach for their explicit construction. As opposed to minimax shrinkage estimators that shrink towards a single prespecified target, minimax multiple shrinkage estimators adaptively shrink towards the more promising of a set of prespecified targets, substantially increasing the region of potential risk reduction while maintaining the protection of always being at least as good as the maximum likelihood estimator. These estimators are particularly useful in practice as they address the challenge of selecting a minimax shrinkage estimator when prior information suggests more than one viable shrinkage target to choose from. In contrast to previous formal Bayes minimax multiple shrinkage estimators, which were built on mixtures of superharmonic marginals, these proper Bayes minimax multiple shrinkage estimators are obtained via mixtures of square-root superharmonic marginals. Examples of such proper Bayes minimax multiple shrinkage estimators include an adaptive convex combination of the rescaled Strawderman shrinkage estimators.
Comments31 pages, 7 figures
