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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Estimates of functionals of stochastic sequences with periodically stationary increments

P. S. Kozak, M. P. Moklyachuk

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Abstract: The problem of optimal estimation of the linear functional depending on the unknown values of a stochastic sequence with periodically stationary increments from observations of the sequence at points Z\{0,1,...,N} is considered. Formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functional are proposed in the case where spectral density is exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed for the given sets of admissible spectral densities.

Keywords: Sequence with periodically stationary increments, robust estimate, mean square error, least favorable spectral density, minimax spectral characteristics

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