UDC 519.21
ON THE PROBLEM OF MINIMAX INTERPOLATION OF STATIONARY SRQUENCES
Abstract. The problem of the mean-square optimal estimation of the linear functionals that depend on the unknown values of a stochastic stationary sequence from observations of the sequence with missing values is considered. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functionals are derived under the condition of spectral determinacy, where the spectral density of the sequence is exactly known. The minimax (robust) method of estimation is applied in the case where the spectral density of the sequence is not known exactly while some sets of admissible spectral densities are given. Formulas that determine the least favourable spectral densities and the minimax spectral characteristics are derived for some special sets of feasible densities.
Keywords: stationary sequence, minimax-robust estimate, least favourable spectral density, minimax spectral characteristic.
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