Minimax-Robust Estimation Problems for Stationary Stochastic Sequences

  • Mikhail Moklyachuk Kyiv National Taras Shevchenko University
Keywords: Stochastic sequence, minimax-robust estimate, mean square error, least favourable spectral density, minimax-robust spectral characteristic

Abstract

This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence with a stationary noise, estimates could be obtained. Formulas for calculating the spectral characteristics and the mean-square errors of the optimal estimates of functionals are derived in the case of spectral certainty, where spectral densities of the sequences are exactly known. In the case of spectral uncertainty, where spectral densities of the sequences are not known exactly while sets of admissible spectral densities are given, the minimax-robust method of estimation is applied. Formulas that determine the least favourable spectral densities and the minimax spectral characteristics of estimates are presented for some special classes of admissible spectral densities.

Author Biography

Mikhail Moklyachuk, Kyiv National Taras Shevchenko University
Department of Probability Theory, Statistics and Actuarial Mathematics, Professor

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Published
2015-11-28
How to Cite
Moklyachuk, M. (2015). Minimax-Robust Estimation Problems for Stationary Stochastic Sequences. Statistics, Optimization & Information Computing, 3(4), 348-419. https://doi.org/10.19139/soic.v3i4.173
Section
Scientific Report