Quadratic risk domination of restricted least squares estimators via Stein-ruled auxiliary constraints
type: Item
instance of: scholarly article
title: Quadratic risk domination of restricted least squares estimators via Stein-ruled auxiliary constraints
zbMATH Open document ID: 0595.62061
DOI: 10.1016/0304-4076(85)90157-5
author: Ron C. Mittelhammer
published in: Journal of Econometrics
publication date: 1985-01-01T00:00:00Z
review text: This paper deals with the linear model \[ y=X\beta +u,\quad R\beta =r\quad and\quad u\sim N(0,\sigma^ 2I_ n). \] If m, the number of unrestricted parameters is at least 3, then the BLUE of \(\beta\) can be improved by a Stein-rule estimator depending on the choice of the used quadratic loss function. The Stein-rule depends on some parameter which is restricted to some interval and is subjected to optimization. Only under special situation the risk gain optimal parameter is independent of unknown parameters. However, the risk gain optimal parameter can be restricted to a finite interval. This interval can be further restricted if it is required that the risk gain difference is an isotonic function of some non-centrality parameter. Also relative risk gain is considered and here a confidence interval procedure is suggested to provide information regarding the actual magnitude of risk reduction achieved.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 3958473
zbMATH Keywords: quadratic risk domination
zbMATH Keywords: restricted least squares estimators
zbMATH Keywords: general linear model
zbMATH Keywords: restricted regression analysis
zbMATH Keywords: BLUE
zbMATH Keywords: Stein-rule estimator
zbMATH Keywords: quadratic loss
zbMATH Keywords: risk gain optimal parameter
zbMATH Keywords: relative risk
zbMATH Keywords: confidence interval procedure
reviewed by: Hilmar Drygas
MaRDI profile type: Publication
full work available at URL: 0304-4076(85)90157-5
OpenAlex ID: W1967913997
cites work: Q4178373
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cites work: A note on estimating the common mean of k normal distributions and the stein problem
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description: scientific article; zbMATH DE number 3958473