The Annals of Statistics

Estimating a Bounded Normal Mean

George Casella and William E. Strawderman

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Abstract

The problem of estimating a normal mean has received much attention in recent years. If one assumes, however, that the true mean lies in a bounded interval, the problem changes drastically. In this paper we show that if the interval is small (approximately two standard deviations wide) then the Bayes rule against a two point prior is the unique minimax estimator under squared error loss. For somewhat wider intervals we also derive sufficient conditions for minimaxity of the Bayes rule against a three point prior.

Article information

Source
Ann. Statist., Volume 9, Number 4 (1981), 870-878.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345527

Digital Object Identifier
doi:10.1214/aos/1176345527

Mathematical Reviews number (MathSciNet)
MR619290

Zentralblatt MATH identifier
0474.62010

JSTOR
links.jstor.org

Subjects
Primary: 62C99: None of the above, but in this section
Secondary: 62F10: Point estimation

Keywords
Minimax normal mean least favorable prior

Citation

Casella, George; Strawderman, William E. Estimating a Bounded Normal Mean. Ann. Statist. 9 (1981), no. 4, 870--878. doi:10.1214/aos/1176345527. https://projecteuclid.org/euclid.aos/1176345527


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