A Paradox Concerning Shrinkage Estimators: Should a Known Scale Parameter Be Replaced by an Estimated Value in the Shrinkage Factor?
AbstractWhen estimating, under quadratic loss, the location parameter[theta]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 fort-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[theta]=0.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 59 (1996)
Issue (Month): 2 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Ouassou, Idir & Strawderman, William E., 2002. "Estimation of a parameter vector restricted to a cone," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 121-129, January.
- D. Fourdrinier & S. Pergamenshchikov, 2007. "Improved Model Selection Method for a Regression Function with Dependent Noise," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(3), pages 435-464, September.
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