Advances and Applications in Statistics
Volume 11, Issue 1, Pages 101 - 136
(February 2009)
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PRELIMINARY TEST AND STEIN-TYPE ESTIMATION OF LOCATION PARAMETER FOR ELLIPTICALLY CONTOURED DISTRIBUTIONS
M. L. Men鮤ez (Spain), L. Pardo (Spain) and K. Zografos (Greece)
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Abstract: We consider the estimation problem of the location parameter in the family of elliptically contoured distributions when a priori it is suspected that its components are equal but unknown. Some preliminary test estimators are defined and its asymptotic distribution is obtained. In order to compare them, a decision-theoretic approach is given using its asymptotic distributional quadratic risk under the null hypothesis (equality in the components of the location parameter) as well as under contiguous alternative hypotheses. It is established that positive-part of Stein-rule estimator is superior to the James-Stein estimator. Other interesting relations between them are obtained. |
Keywords and phrases: elliptically contoured distribution, preliminary test estimator, James-Stein estimator, positive-part of Stein-rule estimator, asymptotic distributional quadratic risk, asymptotic bias. |
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