Affine minimax confidence intervals for a bounded normal mean

Philip B. Stark

Statistics & Probability Letters, 1992, vol. 13, issue 1, 39-44

Abstract: Consider the problem of constructing a fixed-length confidence interval for [theta]0 from the observation Y ~ N([theta]0, [sigma]2), when we know a priori that [theta]0 [epsilon][-[tau], [tau]]. The length of the minimax confidence interval centered at an affine functional of Y can be computed numerically -- this paper gives tables for confidence levels 95%, 99% and 99.9% and a variety of values of the 'signal to noise ratio', . The lengths of minimax confidence intervals centered at arbitrary measurable functionals of Y can be bounded from above and below using the affine results. For sufficiently small values of , the minimax intervals offer arbitrarily large improvements over the standard interval . Asymptotically as [tau]/[sigma]-->[infinity], they offer no improvement. For moderate values 2 [less-than-or-equals, slant] [tau]/gs [less-than-or-equals, slant] 5 and confidence levels between 95% and 99.9%, affine minimax intervals are about 3% to 39% shorter than the standard interval.

Keywords: Bounded; normal; mean; affine; minimax; confidence; intervals; minimax; estimation (search for similar items in EconPapers)
Date: 1992
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