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On the minimax estimator of a bounded normal mean

✍ Scribed by Éric Marchand; François Perron

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
114 KB
Volume
58
Category
Article
ISSN
0167-7152

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✦ Synopsis

For estimating under squared-error loss the mean of a p-variate normal distribution when this mean lies in a ball of radius m centered at the origin and the covariance matrix is equal to the identity matrix, it is shown that the Bayes estimator with respect to a uniformly distributed prior on the boundary of the parameter space ( BU ) is minimax whenever m 6 √ p. Further descriptions of the cuto points of small enough radiuses (i.e., m 6 m 0 (p)) for BU to be minimax are given. These include lower bounds and the large dimension p limiting behaviour of m 0 (p)= √ p. Finally, implications for the associated minimax risk are described.

📜 SIMILAR VOLUMES

A note on admissibility of the maximum l
A note on admissibility of the maximum likelihood estimator for a bounded normal mean
✍ Manabu Iwasa; Yoshiya Moritani 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 279 KB

In estimating a bounded normal mean, it is known that the maximum likelihood estimator is inadmissible for squared error loss function. In this paper, we discuss the admissibility for other loss functions. We prove that the maximum likelihood estimator is admissible under absolute error loss.