多元正态分布均值向量估计的若干探讨

兰州大学机构库 >数学与统计学院

	多元正态分布均值向量估计的若干探讨
Alternative Title	Discussions on Estimation of the Mean Vector of a Multivariate Normal Distribution
	佟瑀
Thesis Advisor	李周平
	2015-05-12
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	学士
Keyword	集成风险收缩估计 James-Stein估计量
Abstract	本文主要内容为在集成风险意义下，对异方差的多元正态分布的均值向量进行估计，并给出Brown， Nie & Xie [1]中一个未解决问题的一种解决方法。首先，先对James-Stein估计量进行简单的介绍，并说明它的误差比使用极大似然估计法得到的估计量的误差在某些情况下要小。然后,给出集成风险以及在集成风险下，极小极大性的定义。之后，讨论几种收缩到0的估计量的集成极小极大性，研究它们在满足何种条件的情况下符合集成极小极大性，并给出对上文所提到的问题的解决方法。最后，我们对James-Stein估计量和极大似然估计量进行数据模拟。
Other Abstract	The article mainly discuss the estimation of the mean vector of a heteroscedastic multivariate normal distribution based on the ensemble risk and give a solution of an unsolved problem in Brown, Nie & Xie [1]. First of all, we introduce the James-Stein estimator, and explain the error of James-Stein estimator is smaller than the MLE estimator. Then we give a definition of the ensemble risk and ensemble minimaxity. After that we discuss the ensemble minimaxity of several kinds of estimators that shrink towards to zero and give the conditions that make them be ensemble minimax. Then we give the solution the above mentioned. Finally, we give the digital simulation of James-Stein estimator and MLE estimator.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/225497
Collection	数学与统计学院
Recommended Citation GB/T 7714	佟瑀. 多元正态分布均值向量估计的若干探讨[D]. 兰州. 兰州大学,2015.

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