Theory of Probability and Mathematical Statistics
Cross-correlogram estimators of impulse response functions
Yu. V. Kozachenko, I. V. Rozora
Download PDF
Abstract: The integral cross-correlogram estimator of the response function for a linear homogeneous system is considered in this paper. An upper bound for the tail of the distribution of the supremum of the estimation error is found. In the proof, we use some properties of square-Gaussian stochastic processes.
Keywords: Correlogram, impulse response function, large deviation probabilities
Bibliography: 1. I. P. Blazhievs'ka, Asymptotic unbiasedness and consistency of correlogram estimators of impulse response functions in linear homogeneous systems, Naukovi Visti NTUU ''KPI'' 4 (2014), 7-12. (Ukrainian)
2. V. V. Buldygin and I. P. Blazhievs'ka, Correlation properties of correlogram estimators of impulse response functions, Naukovi Visti NTUU KPI'' 5 (2009), 120-128. (Ukrainian)
3. V. V. Buldygin and I. P. Blazhievs'ka, Asymptotic properties of correlogram estimators of impulse response functions in linear systems, Naukovi Visti NTUU KPI'' 4 (2010), 16-27. (Ukrainian)
4. I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, ''Nauka'', Moscow, 1977; English transl., Scripta Technica, Inc. W. B. Saunders Co., Philadelphia, Pa.-London-Toronto, Ont. 1969.
5. Yu. V. Kozachenko, A. O. Pashko, and I. V. Rozora, Modelling Stochastic Processes and Ransom Fields, ''Zadruga'', Kyiv, 2007. (Ukrainian)
6. V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, TViMS, Kiev, 1998; English transl., American Mathematical Society, Providence, RI, 2000.
7. V. V. Buldygin and V. G. Kurotschka, On cross-correlogram estimators of the response function in continuous linear systems from discrete observations, Random Oper. Stoch. Equ. 7 (1999), no. 1, 71-90.
8. V. V. Buldygin and Fu Li, On asymptotic normality of an estimation of unit impulse responses of linear system I, Teor. Ĭmovir. Mat. Stat. 54 (1996), 16-24; Enlglish transl. in Theor. Probability and Math. Statist. 54 (1997), 3-17.
9. V. V. Buldygin and Fu Li, On asymptotic normality of an estimation of unit impulse responses of linear system II, Teor. Ĭmovir. Mat. Stat. 55 (1996), 30-37; English transl. in Theor. Probability and Math. Statist. 55 (1997), 30-37.
10. V. Buldygin, F. Utzet, and V. Zaiats, Asymptotic normality of cross-correlogram estimators of the response function, Stat. Inference Stoch. Process. 7 (2004), 1-34.
11. V. Buldygin, F. Utzet, and V. Zaiats, A note on the application of intergals involving cyclic products of kernels, Qüestiió 26, no. 1-2 (2002), 3-14.
12. Yu. V. Kozachenko and O. V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Communications 3 (1998), no. 1, 83-94.
