A statistical minimax approach to optimizing linear models under a priori uncertainty conditions

Authors:
E. Yu. Ignashchenko;A. R. Pankov;K. V. Semenikhin
Affiliations:
Moscow Institute of Aviation (Technical University), Moscow, Russia 125993;Moscow Institute of Aviation (Technical University), Moscow, Russia 125993;Moscow Institute of Aviation (Technical University), Moscow, Russia 125993
Venue:
Journal of Computer and Systems Sciences International
Year:
2010

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Abstract

A statistical minimax method for optimizing linear models with parameters, given up to the accuracy of belonging to some uncertainty sets, is proposed. Statistical methods for constructing uncertainty sets as confidence regions with a given reliability level are presented. A numerical method for finding a minimax strategy is proposed for arbitrary uncertainty sets that meet convexity and compactness conditions. A number of examples are considered that admit the analytical solution to optimization problem. Results of numerical simulation are given.