2019
Том 71
№ 11

All Issues

Asymptotic normality and efficiency of a weighted correlogram

Maiboroda R. E.

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Abstract

For a process X(t)=Σ j=1 M g j (t 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.

English version (Springer): Ukrainian Mathematical Journal 50 (1998), no. 7, pp 1067-1079.

Citation Example: Maiboroda R. E. Asymptotic normality and efficiency of a weighted correlogram // Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 937–947.

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