Extrapolation Problem for Multidimensional Stationary Sequences with Missing Observations
| Autor: | Maria Sidei, Mikhail Moklyachuk, Oleksandr Masyutka |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Mean square Sequence Control and Optimization Optimal estimation Mean squared error Extrapolation Stationary sequence Minimax Stationary sequence mean square error minimax-robust estimate least favorable spectral density minimax spectral characteristic Artificial Intelligence Signal Processing Applied mathematics Computer Vision and Pattern Recognition Statistics Probability and Uncertainty lcsh:Probabilities. Mathematical statistics lcsh:QA273-280 Information Systems Stationary noise Mathematics |
| Zdroj: | Statistics, Optimization and Information Computing, Vol 7, Iss 1, Pp 97-117 (2019) |
| ISSN: | 2310-5070 |
| Popis: | This paper focuses on the problem of the mean square optimal estimation of linear functionals which dependon the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of these quence 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. |
| Databáze: | OpenAIRE |
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