A brief review of shrinkage estimation of a multivariate normal mean with extension to multiple linear regression

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Title:	A brief review of shrinkage estimation of a multivariate normal mean with extension to multiple linear regression
Authors:	林志娟;Lin, Jyh-jiuan;Pal, Nabendu;Chang, Ching-hui
Contributors:	淡江大學統計學系
Keywords:	loss function;prediction mean squared error (PMSE);risk function
Date:	2005-12
Issue Date:	2009-11-30 12:52:41 (UTC+8)
Publisher:	Pushpa Publishing House
Abstract:	Estimation of regression coefficients in a linear regression model is essential not only to understand the relationship between the response (dependent) variable and the explanatory (independent) variables, but also for predicting the response variable efficiently. It is known that an improved shrinkage estimation of the regression coefficients leads to a better prediction of the response variable in terms of lower prediction mean squared error. In this review paper we revisit the shrinkage estimation of the regression coefficients, which is an extension of Stein�s seminal work on shrinkage estimation of a multivariate normal mean, and see its connection to prediction. We have compiled materials from the existing major works on shrinkage estimation and added some new results (or extended some existing less known results) so that our review paper gives a comprehensive idea of the topic and hence helps the researchers interested in this area.
Relation:	Advances and Applications in Statistics 5(3), pp.371-399
Appears in Collections:	[Graduate Institute & Department of Statistics] Journal Article

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