Blazhievska I.P.

Asymptotic Unbiasedness and Consistency of Cross-Correlogram Estimators of Response Functions in Linear Continuous Systems

The estimation problem of an unknown real-valued response function of a linear continuous system is considered. We suppose that a family of zero-mean stationary Gaussian processes, which are close, in some sense, to a white noise, disturbs the system. Integral-type sample input-output cross-correlograms are taken as estimators of the response function from . The corresponding cross-correlogram estimator depends on two parameters (a parameter of a scheme of series and a length of an averaging interval) and is biased.

On correlation properties of the cross-correlogram estimators of impulse response functions

Statistical estimators of unit impulse responses of linear systems under perturbations by Gaussian processes which are different from the white noise are considered. Some properties of correlation functions of estimators are studied in the case when the impulse response function is from the space L2(R).

On asymptotic properties of the crosscorrelogram estimators of impulse response functions in linear systems

In this paper, we consider the cross-correlogram estimators of impulse response functions in linear systems. We hypothesize that the system is disturbed by a family of Gaussian processes close to white noise. We study the asymptotic normality of finite-dimensional distributions of estimators and their asymptotic normality in the space of continuous functions given that the impulse response function belongs to L2R