Asymptotic normality and efficiency of a weighted correlogram
For a process X(t)=Σ j=1 M g j (t)ξ j (), where gj(t) are nonrandom given functions, \((\xi _j (t),j = \overline {1,M} )\) is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r kl(τ), we construct an estimate \(\hat r_{kl} (\tau ,T)\) for the functions r kl(τ...
Збережено в:
| Дата: | 1998 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1998
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4874 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | For a process X(t)=Σ j=1 M g j (t)ξ j (), where gj(t) are nonrandom given functions, \((\xi _j (t),j = \overline {1,M} )\) is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r kl(τ), we construct an estimate \(\hat r_{kl} (\tau ,T)\) for the functions r kl(τ) on the basis of observations X(t), t ∈ [0, T]. We establish conditions for the asymptotic normality of \(\sqrt T (\hat r_{kl} (\tau ,T) - r_{kl} (\tau ))\) as T → ∞. We consider the problem of the optimal choice of parameters of the estimate \(\hat r_{kl} \) depending on observations. |
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