Conditional properties of interval estimators of the normal variance (Q1101157)

The authors have examined both one-sided and two-sided interval estimators for the normal variance when the mean is unknown using conditional criteria and found that most intervals have acceptable conditional properties. In the two-sided case they examine three well- known intervals, namely, equally-tailed, minimum-length and shortest- unbiased (Neyman-shortest), and find the shortest-unbiased interval possessing the strongest conditional properties, and with the minimum- length a close second one. In the one-sided case they find 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).