Asymptotic normality and efficiency of a weighted correlogram - Maiboroda, R. E. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
For a process X(t)=Σ j=1 M g j (t)ξ j (), where gj(t) are nonrandom given functions, \((ξ _j (t),j = \overline {1,M} )\) is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r kl(τ), we construct an estimate \(\hat r_{kl} (τ ,T)\) for the functions r kl(τ) on the basis of observations X(t), t ∈ [0, T]. We establish conditions for the asymptotic normality of \(\sqrt T (\hat r_{kl} (τ ,T) - r_{kl} (τ ))\) as T → ∞. We consider the problem of the optimal choice of parameters of the estimate \(\hat r_{kl} \) depending on observations.