## The Annals of Statistics

### Confidence Intervals for Linear Functions of the Normal Parameters

V. M. Joshi

#### 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

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