Bernoulli

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  • Volume 11, Number 4 (2005), 571-590.

Minimax expected measure confidence sets for restricted location parameters

Steven N. Evans, Ben B. Hansen, and Philip B. Stark

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Abstract

We study confidence sets for a parameter θ∈Θ that have minimax expected measure among random sets with at least 1-α coverage probability. We characterize the minimax sets using duality, which helps to find confidence sets with small expected measure and to bound improvements in expected measure compared with standard confidence sets. We construct explicit minimax expected length confidence sets for a variety of one-dimensional statistical models, including the bounded normal mean with known and with unknown variance. For the bounded normal mean with unit variance, the minimax expected measure 95% confidence interval has a simple form for Θ= [-τ, τ] with τ≤3.25. For Θ= [-3, 3], the maximum expected length of the minimax interval is about 14% less than that of the minimax fixed-length affine confidence interval and about 16% less than that of the truncated conventional interval [X -1.96, X + 1.96] ∩[-3,3].

Article information

Source
Bernoulli Volume 11, Number 4 (2005), 571-590.

Dates
First available in Project Euclid: 7 September 2005

Permanent link to this document
http://projecteuclid.org/euclid.bj/1126126761

Digital Object Identifier
doi:10.3150/bj/1126126761

Mathematical Reviews number (MathSciNet)
MR2158252

Zentralblatt MATH identifier
1092.62040

Keywords
Bayes-minimax duality constrained parameters

Citation

Evans, Steven N.; Hansen, Ben B.; Stark, Philip B. Minimax expected measure confidence sets for restricted location parameters. Bernoulli 11 (2005), no. 4, 571--590. doi:10.3150/bj/1126126761. http://projecteuclid.org/euclid.bj/1126126761.


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