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A note on decision theoretic estimation of ordered parameters

โœ Scribed by George Iliopoulos

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
89 KB
Volume
50
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

This paper deals with decision theoretic estimation of the middle among three ordered location parameters under an arbitrary strictly convex loss function. Double-shrinkage estimators are produced which use all the available data and improve on single-shrinkage ones. The case of estimation of the middle among three ordered scale parameters with the possible existence of nuisance parameters is also discussed.

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The notion of universal admissibility of estimators was introduced and developed by Hwang (1985) and Brown and Hwang (1989). In several models commonly used estimators of scale parameters are shown to be inadmissible under specified loss functions. Here we focus on the scale and location-scale invar