Geodesic
Correlogram estimation of response functions of linear systems in scheme of some independent samples
Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 16-27

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The problem of estimation of an unknown response function from $L_{2}(\mathbf{R})$ of a linear system is considered. The inputs are supposed to be stationary zero-mean Gaussian almost surely sample continuous processes. We take the integral-type sample input-output cross-correlograms as estimators of the response function and apply the scheme of some independent samples, when the pair of inputs and outputs are observed. The asymptotic normality of the distributions of centered cross-correlogram estimations in the space of continuous functions and the construction of the confidence bands for the limiting process are discussed.
Keywords: Response function, sample continuity, sample cross-correlogram, scheme of some independent samples, asymptotic normality. 
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     author = {I. P. Blazhievska},
     title = {Correlogram estimation of response functions of linear systems in scheme of some independent samples},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {16--27},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a2/}
}
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I. P. Blazhievska. Correlogram estimation of response functions of linear systems in scheme of some independent samples. Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 16-27. http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a2/