The Annals of Statistics

Improved Invariant Confidence Intervals for a Normal Variance

Constantinos Goutis and George Casella

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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.

Article information

Ann. Statist., Volume 19, Number 4 (1991), 2015-2031.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F25: Tolerance and confidence regions
Secondary: 62C99: None of the above, but in this section

Normal distribution coverage probability posterior probability


Goutis, Constantinos; Casella, George. Improved Invariant Confidence Intervals for a Normal Variance. Ann. Statist. 19 (1991), no. 4, 2015--2031. doi:10.1214/aos/1176348384.

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