Open Access
Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 62F25
Secondary: 62F05

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

Rights: Copyright © 1976 Institute of Mathematical Statistics

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.4 • No. 2 • March, 1976
Back to Top