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New classes of improved confidence intervals for the variance of a normal distribution

Research paper by Constantinos Petropoulos, Stavros Kourouklis

Indexed on: 14 Dec '10Published on: 14 Dec '10Published in: Metrika



Abstract

Two new classes of improved confidence intervals for the variance of a normal distribution with unknown mean are constructed. The first one is a class of smooth intervals. Within this class, a subclass of generalized Bayes intervals is found which contains, in particular, the Brewster and Zidek-type interval as a member. The intervals of the second class, though non-smooth, have a very simple and explicit functional form. The Stein-type interval is a member of this class and is shown to be empirical Bayes. The construction extends Maruyama’s (Metrika 48:209–214, 1998) point estimation technique to the interval estimation problem.