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.
Publié le : 1976-03-14
Classification:
Confidence intervals,
linear functions of mean and variance,
modified Bessel functions,
62F25,
62F05
@article{1176343419,
author = {Joshi, V. M.},
title = {Confidence Intervals for Linear Functions of the Normal Parameters},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 413-418},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343419}
}
Joshi, V. M. Confidence Intervals for Linear Functions of the Normal Parameters. Ann. Statist., Tome 4 (1976) no. 1, pp. 413-418. http://gdmltest.u-ga.fr/item/1176343419/