On asymptotic normality of estimators of unit impulse responses of linear systems. II. (English. Russian original) Zbl 0927.62097

Buldygin, V. V.; Fu, Li

Theory Probab. Math. Stat. 55, 29-36 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 30-37 (1996).

[For part I see the preceding entry, Zbl 0927.62096]
Let \(X_\triangle=\{X_\triangle(t),\;t \in R\}\) be a measurable stationary Gaussian process with \(E X_\triangle(t)=0\) and let \[ Y_\triangle(t)=\int_0^{\infty}H(s)X_\triangle(t-s)ds,\;\;t\in R. \] The authors investigate the properties of the estimator \[ \widehat H_{T,\triangle}(\tau)=(cT)^{-1} \int_0^T X_\triangle(t)Y_\triangle(t+\tau)dt \] of the impulse function \(H(\tau)\) and the behaviour of the process \[ Z_{T,\triangle}(\tau)=\sqrt{T}(\widehat H_{T,\triangle}(\tau)-E\widehat H_{T,\triangle}(\tau)), \;\;\tau \geq 0. \] They prove the asymptotic normality of the processes \(Z_{T,\triangle}\) and \(W_{T,\triangle}(\tau)=\sqrt{T}(\widehat H_{T,\triangle}(\tau)-H(\tau)).\)

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

62M20	Inference from stochastic processes and prediction
62G20	Asymptotic properties of nonparametric inference
60G35	Signal detection and filtering (aspects of stochastic processes)

Keywords:

linear systems; impulse functions; asymptotic normality

Citations:

Zbl 0927.62096