TY - JOUR
T1 - A paradox concerning shrinkage estimators
T2 - Should a known scale parameter be replaced by an estimated value in the shrinkage factor?
AU - Fourdrinier, Dominique
AU - Strawderman, William E.
N1 - Funding Information:
Received March 19, 1996. AMS 1991 subject classification: 62F10, 62H12, 62C20. Key words and phrases: spherical symmetry, quadratic loss, James Stein estimation, location parameter, minimaxity, robustness. * Research supported by National Science Foundation Grants DMS-9307727 and DMS-9400476.
PY - 1996/11
Y1 - 1996/11
N2 - When estimating, under quadratic loss, the location parameter θ of a spherically symmetric distribution with known scale parameter, we show that it may be that the common practice of utilizing the residual vector as an estimate of the variance is preferable to using the known value of the variance. In the context of Stein-like shrinkage estimators, we exhibit sufficient conditions on the spherical distributions for which this paradox occurs. In particular, we show that it occurs for t-distributions when the dimension of the residual vector is sufficiently large. The main tools in the development are upper and lower bounds on the risks of the James-Stein estimators which are exact at θ= 0.
AB - When estimating, under quadratic loss, the location parameter θ of a spherically symmetric distribution with known scale parameter, we show that it may be that the common practice of utilizing the residual vector as an estimate of the variance is preferable to using the known value of the variance. In the context of Stein-like shrinkage estimators, we exhibit sufficient conditions on the spherical distributions for which this paradox occurs. In particular, we show that it occurs for t-distributions when the dimension of the residual vector is sufficiently large. The main tools in the development are upper and lower bounds on the risks of the James-Stein estimators which are exact at θ= 0.
KW - James-stein estimation
KW - Location parameter
KW - Minimaxity
KW - Quadratic loss
KW - Robustness
KW - Spherical symmetry
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U2 - 10.1006/jmva.1996.0056
DO - 10.1006/jmva.1996.0056
M3 - Article
AN - SCOPUS:0030295571
SN - 0047-259X
VL - 59
SP - 109
EP - 140
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 2
ER -