Minimax filtration of linear transformations of stationary consequences
We will consider the problem of determining a linear, mean-square optimal estimate of the transformation $A\xi = \sum_{j=0}^{\infty}a(j)\xi(-j)$ of a stationary random sequence $\xi(k)$ with density $f (\lambda)$ from observations of the sequence $\xi(k)+\eta(k)$ with $k\leq 0$, where $\eta(k)$ is...
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| Datum: | 1991 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1991
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9310 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We will consider the problem of determining a linear, mean-square optimal estimate of the transformation $A\xi = \sum_{j=0}^{\infty}a(j)\xi(-j)$ of a stationary random sequence $\xi(k)$ with density $f (\lambda)$ from observations of the sequence $\xi(k)+\eta(k)$ with $k\leq 0$, where $\eta(k)$ is a stationary sequence not correlated with $\xi (k)$ with density $g(\lambda)$. The least favorable spectral densities $f_0(\lambda)\in D_f$, $g_0(\lambda)\in D_g$, and minimax (robust) spectral characteristics of an optimal estimate $A\xi$ for different classes of densities $D_f$, $D_g$. |
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