Both one-sided and two-sided interval estimators are examined using conditional criteria and we find that most common intervals have acceptable conditional properties. In the two-sided case we further examine three well known intervals and find the shortest-unbiased (Neyman-shortest) interval possessing the strongest conditional properties, with the minimum-length interval a close second. In the one-sided case we have the somewhat surprising result that the lower confidence interval (which results from inverting the UMP test of $H_0: \sigma \leq \sigma_0$) has weaker conditional properties than the upper interval (where a UMP test does not exist).
Publié le : 1987-12-14
Classification:
Confidence,
normal distribution,
betting procedures,
62F25,
62C99
@article{1176350599,
author = {Maatta, Jon M. and Casella, George},
title = {Conditional Properties of Interval Estimators of the Normal Variance},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 1372-1388},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350599}
}
Maatta, Jon M.; Casella, George. Conditional Properties of Interval Estimators of the Normal Variance. Ann. Statist., Tome 15 (1987) no. 1, pp. 1372-1388. http://gdmltest.u-ga.fr/item/1176350599/