The Annals of Statistics
- Ann. Statist.
- Volume 4, Number 2 (1976), 413-418.
Confidence Intervals for Linear Functions of the Normal Parameters
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.
Ann. Statist., Volume 4, Number 2 (1976), 413-418.
First available in Project Euclid: 12 April 2007
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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