Interpolation Problem for Stationary Sequences with Missing Observations
| Autor: | Mikhail Moklyachuk, Maria Sidei |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Sequence Control and Optimization 010102 general mathematics Spectral density Stationary sequence Stationary sequence mean square error minimax-robust estimate least favorable spectral density minimax spectral characteristic 01 natural sciences Combinatorics 010104 statistics & probability Artificial Intelligence Signal Processing Computer Vision and Pattern Recognition lcsh:Probabilities. Mathematical statistics 0101 mathematics Statistics Probability and Uncertainty lcsh:QA273-280 Information Systems Mathematics Interpolation |
| Zdroj: | Statistics, Optimization and Information Computing, Vol 3, Iss 3, Pp 259-275 (2015) |
| ISSN: | 2310-5070 2311-004X |
| DOI: | 10.19139/soic.v3i3.149 |
| Popis: | The problem of the mean-square optimal estimation of the linear functional $A_s\xi=\sum\limits_{l=0}^{s-1}\sum\limits_{j=M_l}^{M_l+N_{l+1}}a(j)\xi(j),$ $M_l=\sum\limits_{k=0}^l (N_k+K_k),$ \, $N_0=K_0=0,$ which depends on the unknown values of a stochastic stationary sequence $\xi(k)$ from observations of the sequence at points of time $j\in\mathbb{Z}\backslash S $, $S=\bigcup\limits_{l=0}^{s-1}\{ M_{l}, M_{l}+1, \ldots, M_{l}+N_{l+1} \}$ is considered. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functional are derived under the condition of spectral certainty, where the spectral density of the sequence $\xi(j)$ is exactly known. The minimax (robust) method of estimation is applied in the case where the spectral density is not known exactly, but sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are derived for some special sets of admissible densities. |
| Databáze: | OpenAIRE |
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