论文标题
Frechet的Stein效应意味着
The Stein Effect for Frechet Means
论文作者
论文摘要
特里切特平均值是对不一定是向量空间的度量分布的位置的有用描述。本文从决策理论的角度考虑了多个特征平均值的同时估计，尤其是詹姆斯·斯坦·斯坦收缩估计剂的概括可以主导着平均均值的无偏估计量的程度。结果表明，如果度量空间满足非阳性曲率条件，那么随着空间尺寸的增长，这种广义的James-Stein估计量渐近地主导了无偏的估计器。这些结果适用于在包括希尔伯特空间在内的各种空间上的大量分布，因此部分扩展了有关詹姆斯 - 斯坦估计量在欧几里得空间上非正常分布的适用性的已知结果。进行了公制树和对称阳性限定矩阵的仿真研究，从数值上证明了这种广义的詹姆斯 - 斯坦估计量的疗效。
The Frechet mean is a useful description of location for a probability distribution on a metric space that is not necessarily a vector space. This article considers simultaneous estimation of multiple Frechet means from a decision-theoretic perspective, and in particular, the extent to which the unbiased estimator of a Frechet mean can be dominated by a generalization of the James-Stein shrinkage estimator. It is shown that if the metric space satisfies a non-positive curvature condition, then this generalized James-Stein estimator asymptotically dominates the unbiased estimator as the dimension of the space grows. These results hold for a large class of distributions on a variety of spaces - including Hilbert spaces - and therefore partially extend known results on the applicability of the James-Stein estimator to non-normal distributions on Euclidean spaces. Simulation studies on metric trees and symmetric-positive-definite matrices are presented, numerically demonstrating the efficacy of this generalized James-Stein estimator.
