Estimates of functionals constructed from random sequences with periodically stationary increments

Kozak, P.; Moklyachuk, M.

doi:10.1090/tpms/1050

Estimates of functionals constructed from random sequences with periodically stationary increments

Authors: P. S. Kozak and M. P. Moklyachuk
Translated by: N. N. Semenov
Journal: Theor. Probability and Math. Statist. 97 (2018), 85-98
MSC (2010): Primary 60G10, 60G25, 60G35; Secondary 62M20, 93E10, 93E11
DOI: https://doi.org/10.1090/tpms/1050
Published electronically: February 21, 2019
MathSciNet review: 3746001
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Abstract: The problem of the optimal estimation of the linear functional \begin{equation*} A_N{\xi }=\sum _{k=0}^Na(k)\xi (k) \end{equation*} is studied. The functional depends on unknown values of a random sequence $\xi (k)$ with periodically stationary increments. The estimate is constructed from observations of this sequence at points $\mathbb Z\setminus \{0,1,\dots ,N\}$. Expressions for evaluating the mean square error and spectral characteristics are found for the optimal estimate of the functional in the case where the spectral density of the sequence is known. For a given set of admissible spectral densities, the sets of least favorable spectral densities are found and the spectral characteristics of the optimal estimate of the functional are determined.

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