Weak Versus Strong Dominance of Shrinkage Estimators

Giuseppe De Luca; Jan R. Magnus

doi:10.1007/s40953-021-00270-y

Weak Versus Strong Dominance of Shrinkage Estimators

Giuseppe De Luca, Jan R. Magnus^*

^*Corresponding author for this work

Econometrics and Data Science

Research output: Contribution to Journal › Article › Academic › peer-review

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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.

Original language	English
Pages (from-to)	S239-S266
Number of pages	28
Journal	Journal of Quantitative Economics
Volume	19
Issue number	Suppl 1
Early online date	18 Nov 2021
DOIs	https://doi.org/10.1007/s40953-021-00270-y
Publication status	Published - Dec 2021

Bibliographical note

Funding Information:
We are grateful to the Guest Editors of this special issue and to two referees for comments and suggestions. We are especially grateful to Akio Namba for providing the key to proving Proposition . Without his help this result would have remained a conjecture. Giuseppe De Luca acknowledges financial support from the MIUR PRIN PRJ-0324.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to The Indian Econometric Society.

Keywords

C13
C51
Dominance
James–Stein
Shrinkage

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10.1007/s40953-021-00270-y

Weak Versus Strong Dominance of Shrinkage EstimatorsFinal published version, 1.73 MBLicence: Article 25fa Dutch Copyright Act

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Weak Versus Strong Dominance of Shrinkage Estimators

Abstract

Bibliographical note

Keywords

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