Weak Versus Strong Dominance of Shrinkage Estimators

Tinbergen Institute Discussion Paper 2021-007/III

d/SEAS Working Paper Forthcoming

32 Pages Posted: 26 Jan 2021

See all articles by Giuseppe De Luca

Giuseppe De Luca

University of Palermo - d/SEAS

J.R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics

Date Written: January 14, 2021

Abstract

We consider the estimation of the mean of a multivariate normal distribution with known variance. Most studies consider the risk of competing estimators, that is the trace of the mean squared error matrix. In contrast we consider the whole mean squared error matrix, in particular its eigenvalues. We prove that there are only two distinct eigenvalues and apply our findings to the James--Stein and the Thompson class of estimators. It turns out that the famous Stein paradox is no longer a paradox when we consider the whole mean squared error matrix rather than only its trace.

Keywords: Shrinkage, Dominance, James-Stein

JEL Classification: C13, C51

Suggested Citation

De Luca, Giuseppe and Magnus, Jan R., Weak Versus Strong Dominance of Shrinkage Estimators (January 14, 2021). Tinbergen Institute Discussion Paper 2021-007/III, d/SEAS Working Paper Forthcoming, Available at SSRN: https://ssrn.com/abstract=3766347 or http://dx.doi.org/10.2139/ssrn.3766347

Giuseppe De Luca (Contact Author)

University of Palermo - d/SEAS ( email )

Viale delle Scienze, edificio 13
Palermo, 90124
Italy

Jan R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

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