Minimax-robust estimation technique

Description of methods of estimation of linear functionals of the unknown values of vector-valued stationary stochastic sequences and processes is presented. Extrapolation, interpolation and filtering problems are investigated. Two main approaches to solution of the estimation problems are developed. The first one, the spectral certainty case, is based on the assumption that matrices of spectral densities of stochastic sequences and processes are known exactly. In this case we derived formulas for calculation the spectral characteristics and mean-square errors of the optimal estimates of the functionals which determine the extrapolation, interpolation and filtering problems for stochastic sequences and processes. The second one, the case of spectral uncertainty, is based on assumption that matrices of spectral densities of the processes are not known exactly, but, instead, classes of admissible values of spectral densities are specified. These classes of densities describe different models of vector-valued stationary stochastic processes.

Autorentext

Dr Mikhail P. Moklyachuk is Professor of the Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, Ukraine.Dr Oleksandr Yu. Masyutka is Ass. Professor of the Department ofMathematics and Theoretical Radiophysics, Kyiv National Taras ShevchenkoUniversity, Ukraine.