## The Annals of Statistics

### Improved Invariant Confidence Intervals for a Normal Variance

#### Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348384

Digital Object Identifier
doi:10.1214/aos/1176348384

Mathematical Reviews number (MathSciNet)
MR1135162

Zentralblatt MATH identifier
0745.62026

JSTOR
links.jstor.org

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1176348384