Improved estimation of state of stochastic systems via invariant embedding technique

Authors:
Nicholas A. Nechval;Gundars Berzins;Maris Purgailis;Konstantin N. Nechval
Affiliations:
Department of Mathematical Statistics, University of Latvia, Riga, Latvia;Department of Mathematical Statistics, University of Latvia, Riga, Latvia;Department of Mathematical Statistics, University of Latvia, Riga, Latvia;Department of Applied Mathematics, Transport and Telecommunication Institute, Riga, Latvia
Venue:
WSEAS Transactions on Mathematics
Year:
2008

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Abstract

In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function 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 estimator, which has smaller risk than any of the well-known estimators. Also the problem of how to select the total number of the observations optimally when a constant cost is incurred for each observation taken is discussed. To illustrate the proposed technique, examples are given.