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Stein phenomena and further development on shrinkage methods

斯坦因现象和收缩方法的进一步发展

基本信息

批准号：
13680369
负责人：
KONNO Yoshihiko
金额：
$ 2.24万
依托单位：
Japan Women's University (2003-2004)Chiba University (2001-2002)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

It is well-known that the sample mean and the sample covariance matrix are inadmissible under assumption of normality and appropriate loss function (This is called Stein effect or shrinkage methods.). Since discovery of this phenomenon, there has been a large body of studies on this topic. Furthermore, there has been a broad attention on so called Stein's unbiased risk estimate (SURE), which has been originally proposed for a method to evaluate risk function of estimators under consideration, beyond the original purpose. Although such new development has been reported recently, there are many problems in multivariate analysis with complex structure to be considered based on shrinkage method. The purpose of our research is to develop shrinkage method in complex multivariate model.In this year we investigate on following statistical models and develop shrinkage estimators :(1)We have considered the problem of estimating common regression coefficient matrix of two growth curve models and proposed new shrinkage estimators. Furthermore, we demonstrate numerical experiment to indicate that our proposed estimators have better performance over known estimators.(2)We have considered the problem of estimating a precision matrix of the multivariate normal distribution under the squared loss function and obtained improved estimators.(3)Applying theory of symmetric cones and generalized Wishart distributions, we have developed improved estimation method including the problem of estimating covariance matrix of complex Wishart distribution.

众所周知，在正态性假设和适当的损失函数下，样本均值和样本协方差矩阵是不可接受的（这称为斯坦因效应或收缩方法）。自从发现这种现象以来，人们对这个话题进行了大量的研究。此外，所谓的斯坦因无偏风险估计（SURE）受到了广泛的关注，该估计最初是为了评估所考虑的估计器的风险函数的方法而提出的，超出了最初的目的。虽然最近有这样的新进展报道，但基于收缩法的复杂结构多元分析还存在许多问题需要考虑。我们研究的目的是开发复杂多元模型中的收缩方法。今年我们研究了以下统计模型并开发了收缩估计器：（1）我们考虑了估计两个增长曲线模型的共同回归系数矩阵的问题，并提出了新的收缩估计器。此外，我们的数值实验表明，我们提出的估计器比已知的估计器具有更好的性能。（2）我们考虑了平方损失函数下估计多元正态分布的精度矩阵的问题，并获得了改进的估计器。（3）应用对称锥理论和广义Wishart分布，我们开发了改进的估计方法，包括估计复杂Wishart分布的协方差矩阵的问题。