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

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.