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March, 1976 Confidence Intervals for Linear Functions of the Normal Parameters
V. M. Joshi
Ann. Statist. 4(2): 413-418 (March, 1976). DOI: 10.1214/aos/1176343419


Uniformly most accurate level $1 - \alpha$ confidence procedures for a linear function $\mu + \lambda\sigma^2$ with known $\lambda$ for the parameters of a normal distribution defined by Land were previously shown for both the one-sided and two-sided procedures to be always intervals for $\nu \geqq 2, \nu$ being the number of degrees of freedom for estimating $\sigma^2$. These results are shown in this paper to hold also in the case $\nu = 1$. During the course of the argument a new inequality is obtained relating to the modified Bessel functions which is of independent interest.


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V. M. Joshi. "Confidence Intervals for Linear Functions of the Normal Parameters." Ann. Statist. 4 (2) 413 - 418, March, 1976.


Published: March, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0328.62025
MathSciNet: MR411036
Digital Object Identifier: 10.1214/aos/1176343419

Primary: 62F25
Secondary: 62F05

Keywords: confidence intervals , linear functions of mean and variance , modified Bessel functions

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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