Displaying similar documents to “Confidence regions of minimal area for the scale-location parameter and their applications”

Numerical methods for linear minimax estimation

Norbert Gaffke, Berthold Heiligers (2000)

Discussiones Mathematicae Probability and Statistics

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We discuss two numerical approaches to linear minimax estimation in linear models under ellipsoidal parameter restrictions. The first attacks the problem directly, by minimizing the maximum risk among the estimators. The second method is based on the duality between minimax and Bayes estimation, and aims at finding a least favorable prior distribution.

Asymptotic analysis of minimum volume confidence regions for location-scale families

M. Alama-Bućko, A. Zaigraev (2006)

Applicationes Mathematicae

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An asymptotic analysis, when the sample size n tends to infinity, of the optimal confidence region established in Czarnowska and Nagaev (2001) is considered. As a result, two confidence regions, both close to the optimal one when n is sufficiently large, are suggested with a mild assumption on the distribution of a location-scale family.

Some investigations in minimax estimation theory

Stanisław Trybuła

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1. IntroductionThough the theory of minimax estimation was originated about thirty five years ago (see [7], [8], [9], [23]), there are still many unsolved problems in this area. Several papers have been devoted to statistical games in which the set of a priori distributions of the parameter was suitably restricted ([2], [10], [13]). Recently, special attention was paid to the problem of admissibility ([24], [3], [11], [12]).This paper is devoted to the problem of determining minimax...

Sequential estimation of powers of a scale parameter from delayed observations

Agnieszka Stępień-Baran (2009)

Applicationes Mathematicae

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The problem of sequentially estimating powers of a scale parameter in a scale family and in a location-scale family is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under a scale invariant loss function and with the observation cost determined by a convex function of the stopping time and the number of observations up to that time.