Invariant embedding technique and its applications for improvement or optimization of statistical decisions

Authors:
Nicholas Nechval;Maris Purgailis;Gundars Berzins;Kaspars Cikste;Juris Krasts;Konstantin Nechval
Affiliations:
University of Latvia, EVF Research Institute, Statistics Department, Riga, Latvia;University of Latvia, EVF Research Institute, Statistics Department, Riga, Latvia;University of Latvia, EVF Research Institute, Statistics Department, Riga, Latvia;University of Latvia, EVF Research Institute, Statistics Department, Riga, Latvia;University of Latvia, EVF Research Institute, Statistics Department, Riga, Latvia;Transport and Telecommunication Institute, Applied Mathematics Departmen, Riga, Latvia
Venue:
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
Year:
2010

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Abstract

In the present paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, application examples are given.