Weak versus strong dominance of shrinkage estimators

Giuseppe De Luca () and Jan R. Magnus
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Jan R. Magnus: Vrije Universiteit Amsterdam

No 21-007/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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 (search for similar items in EconPapers)
JEL-codes: C13 C51 (search for similar items in EconPapers)
Date: 2021-01-14
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Weak Versus Strong Dominance of Shrinkage Estimators (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20210007

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