Open Access
December, 1991 Improved Invariant Confidence Intervals for a Normal Variance
Constantinos Goutis, George Casella
Ann. Statist. 19(4): 2015-2031 (December, 1991). DOI: 10.1214/aos/1176348384


Confidence intervals for the variance of a normal distribution with unknown mean are constructed which improve upon the usual shortest interval based on the sample variance alone. These intervals have guaranteed coverage probability uniformly greater than a predetermined value $1-\alpha$ and have uniformly shorter length. Using information relating the size of the samples mean to that of the sample variance, we smoothly shift the usual minimum length interval closer to zero, simultaneously bringing the endpoints closer to each other. The gains in coverage probability and expected length are also investigated numerically. Lastly, we examine the posterior probabilities of the intervals, quantities which can be used as post-data confidence reports.


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Constantinos Goutis. George Casella. "Improved Invariant Confidence Intervals for a Normal Variance." Ann. Statist. 19 (4) 2015 - 2031, December, 1991.


Published: December, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62026
MathSciNet: MR1135162
Digital Object Identifier: 10.1214/aos/1176348384

Primary: 62F25
Secondary: 62C99

Keywords: coverage probability , normal distribution , posterior probability

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1991
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