Nonstandard Variational Problems in Mathematical Statistics

A. M. Shurygin

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: Forty years of very intensive search for robust estimators that ought to be stable to small variations of the model probability density function have achieved modest success. An optimal stable estimator has not been found even for the normal distribution center: the estimators depend on unestimated parameters. The reason lies in traditional methods of mathematical statistics that were used for the solution of a nonstandard problem. The application of the methods of the calculus of variations and functional differentiation reduces the problem to a nonstandard problem in the calculus of variations and, after its solution, makes the problem simple and allows one to obtain a compact optimal solution for an arbitrary parameter of any distribution.

UDC: 519.213

Received in December 2000

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 365–372

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