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Mathematics > Statistics Theory

arXiv:2511.07228 (math)
[Submitted on 10 Nov 2025]

Title:Extrapolation Problem for Multidimensional Stationary Sequences with Missing Observations

Authors:Oleksandr Masyutka, Mikhail Moklyachuk, Maria Sidei
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Abstract:This paper focuses on the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence.
Estimates are based on observations of the sequence with an additive stationary noise sequence.
The aim of the paper is to develop methods of finding the optimal estimates of the functionals in the case of missing observations.
The problem is investigated in the case of spectral certainty where the spectral densities of the sequences are exactly known.
Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived under the condition of spectral certainty.
The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities of the sequences are not known exactly while sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special sets of admissible densities.
Subjects: Statistics Theory (math.ST)
MSC classes: 60G10, 60G25, 60G35, 62M20, 93E10, 93E11
Cite as: arXiv:2511.07228 [math.ST]
  (or arXiv:2511.07228v1 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2511.07228
Journal reference: Statistics Opt. Inform. Comput., Vol. 7, March 2019, pp 97-117
Related DOI: https://doi.org/10.19139/soic.v7i1.527

Submission history

From: Mikhail Moklyachuk [view email]
[v1] Mon, 10 Nov 2025 15:47:37 UTC (22 KB)
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