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Estimation of a parameter vector restricted to a cone

✍ Scribed by Idir Ouassou; William E. Strawderman

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
117 KB
Volume
56
Category
Article
ISSN
0167-7152

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✦ Synopsis

We study estimation of a location vector restricted to a convex cone when the dimension, p, is at least 3. We ΓΏnd estimators which improve on the "usual" estimator (the MLE in the normal case) in the general case of a spherically symmetric distribution with unknown scale. The improved estimators may be viewed as Stein-type shrinkage estimators on the set where the usual unbiased estimator (in the unrestricted case) satisΓΏes the restriction. The improved procedures have the extremely strong property of improving on the "usual" estimator uniformly and simultaneously for all spherically symmetric distributions.

πŸ“œ SIMILAR VOLUMES

Estimation of a parameter vector when so
Estimation of a parameter vector when some components are restricted
✍ Dominique Fourdrinier; Idir Ouassou; William E. Strawderman πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 196 KB

We consider the problem of estimating a p-dimensional parameter y ¼ ðy 1 ; y; y p Þ when the observation is a p þ k vector ðX ; UÞ where dim X ¼ p and where U is a residual vector with dim U ¼ k: The distributional assumption is that ðX ; UÞ has a spherically symmetric distribution around ðy; 0Þ: Tw