ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60, 62, 49 Moklyachuk, Mikhail, Kyiv University, Ukraine Game theory and convex optimization methods in robust estimation With the help of the traditional methods of extrapolation, interpolation and filtering of stochastic processes the spectral characteristic h(f, g) and the mean square error Δ(f, g) of the optimal estimate of the transformation Aξ of a stochastic process ξ(k) from observations of the process ξ(k) + η(k) can be found in the case where the spectral densities f(λ) and g(λ) of the processes ξ(k) and η(k) are known. In practice, however, problems of estimation arise where it is necessary to search the estimate which has the least value of the error for all densities from a certain class of possible spectral densities (see a survey by S. A. Kassam and H. V. Poor (1985)). The spectral characteristic of such an estimate is called minimax-robust. We apply convex optimization and game theory methods to determine the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of the transformation Aξ. Reference: S. A. Kassam, and H. V. Poor, Robust techniques for signal processing. A Survey, Proc. IEEE. 73 (1985), 433–481.