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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Patras, 26 500, Rio, Patras, Greece

    Constantinos Petropoulos & Stavros Kourouklis

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  1. Constantinos Petropoulos
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  2. Stavros Kourouklis
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Correspondence to Constantinos Petropoulos.

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Petropoulos, C., Kourouklis, S. New classes of improved confidence intervals for the variance of a normal distribution. Metrika 75, 491–506 (2012). https://doi.org/10.1007/s00184-010-0338-0

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  • DOI: https://doi.org/10.1007/s00184-010-0338-0

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