Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/229713
Authors: 
De Luca, Giuseppe
Magnus, Jan R.
Year of Publication: 
2021
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2021-007/III
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.
Subjects: 
Shrinkage
Dominance
James-Stein
JEL: 
C13
C51
Document Type: 
Working Paper

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