The Annals of Statistics

Confidence Intervals for Linear Functions of the Normal Parameters

V. M. Joshi

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 4, Number 2 (1976), 413-418.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343419

Digital Object Identifier
doi:10.1214/aos/1176343419

Mathematical Reviews number (MathSciNet)
MR411036

Zentralblatt MATH identifier
0328.62025

JSTOR
links.jstor.org

Subjects
Primary: 62F25: Tolerance and confidence regions
Secondary: 62F05: Asymptotic properties of tests

Keywords
Confidence intervals linear functions of mean and variance modified Bessel functions

Citation

Joshi, V. M. Confidence Intervals for Linear Functions of the Normal Parameters. Ann. Statist. 4 (1976), no. 2, 413--418. doi:10.1214/aos/1176343419. https://projecteuclid.org/euclid.aos/1176343419


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