Open Access
Aug 2005 Minimax expected measure confidence sets for restricted location parameters
Steven N. Evans, Ben B. Hansen, Philip B. Stark
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Bernoulli 11(4): 571-590 (Aug 2005). DOI: 10.3150/bj/1126126761


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].


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Steven N. Evans. Ben B. Hansen. Philip B. Stark. "Minimax expected measure confidence sets for restricted location parameters." Bernoulli 11 (4) 571 - 590, Aug 2005.


Published: Aug 2005
First available in Project Euclid: 7 September 2005

zbMATH: 1092.62040
MathSciNet: MR2158252
Digital Object Identifier: 10.3150/bj/1126126761

Keywords: Bayes-minimax duality , constrained parameters

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

Vol.11 • No. 4 • Aug 2005
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