Geodesic
On asymptotic behavior of the error term in cross-correlogram estimation of response functions in linear systems
Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 5-11

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The problem of estimation of an unknown response function of a linear system with inner noises is considered. We suppose that the response function of the system belongs to $L_{2}({\mathbb R})$. Integral-type sample input-output cross-correlograms are taken as estimators of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes that are close, in some sense, to a white noise. Both the asymptotic normality of finite-dimensional distributions of the normalized error term in the cross-correlogram estimation and the asymptotic normality in the space of continuous functions are discussed.
Keywords: Response function, sample cross-correlogram, asymptotic normality. 
@article{THSP_2010_16_2_a1,
     author = {I. P. Blazhievska},
     title = {On asymptotic behavior of the error term in cross-correlogram estimation of response functions in linear systems},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {5--11},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a1/}
}
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I. P. Blazhievska. On asymptotic behavior of the error term in cross-correlogram estimation of response functions in linear systems. Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 5-11. http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a1/