## The Annals of Statistics

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

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

#### 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