A Criterion for Testing Hypothesis about Impulse Response Function

  • Iryna Rozora National Taras Shevchenko University of Kyiv
  • Yu. V Kozachenko Taras Shevchenko National University of Kyiv
DOI: https://doi.org/10.19139/soic.v4i3.222
Keywords: Impulse response function, cross-correlogram, Hermite polynomials, large deviation probability, rate of convergence, criterion for testing hypothesis

Abstract

In this paper a time-invariant continuous linear system  with a real-valued impulse response function is considered.  A new method for the estimator construction  of the impulse response function is proposed. Two criteria on the shape of the impulse response function are given. In this paper a time-invariantcontinuous linear system  with a real-valued impulse response function is considered.  A new method for the estimator construction  of the impulse response function is proposed. Two criteria on the shape of the impulse response function are given.

Author Biographies

Iryna Rozora, National Taras Shevchenko University of Kyiv
Department of Applied Statistics, Associate Professor
Yu. V Kozachenko, Taras Shevchenko National University of Kyiv
Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mathematics and Mechanics

References

H. Akaike, On the statistical estimation of the frequence response function of a system having multiple input, Ann. Inst. Statist. Math., vol. 17, pp. 185–210, 1965.

H. Akaike, On the use of non-Gaussian process in the identification of a linear dynamic system, Ann. Inst. Statist. Math., vol. 18, pp. 269–276, 1966.

J. S. Bendat, and A.G. Piersol, Engineering Applications of Correlation and Spectral Analysis, Wiley, New York, 1980.

I.P. Blazhievska, Asymptotic unbiasedness and consystency of cross-correlogram estimator for impulse response functions of linear system, Naukovi Visti NTUU KPI? vol. 4, pp. 7–12, 2014.(in Ukrainian)

V.V. Buldygin, and I.P. Blazhievska, On correlation properties of the cross-correlogram estimators of impulse response functions, Naukovi Visti NTUU KPI? vol. 5, pp. 120–128, 2009.(in Ukrainian)

V.V. Buldygin, and I.P. Blazhievska, Asymptotic properties of cross-correlogram estimator for impulse response functions of linear system, Naukovi Visti NTUU KPI? vol. 4, pp. 16–27, 2010.(in Ukrainian)

V.V. Buldygin, and Yu.V. Kozachenko, Metric characterization of random variables and random processes, Amer. Math. Soc., Providence, RI, 2000.

V.V. Buldygin, and V.G. Kurotschka, On cross-coorrelogram estimators of the response function in continuous linear systems from discrete observations, Random Oper. and Stoch. Equ., vol.7, no. 1, pp. 71–90, 1999.

V.V. Buldygin, and Fu Li, On asymptotic normality of an estimation of unit impulse responses of linear system I Theor. Probability and Math. Statist., vol. 54, pp. 3–17, 1997.

V.V. Buldygin, and Fu Li, On asymptotic normality of an estimation of unit impulse responses of linear system II Theor. Probability and Math. Statist., vol. 55, pp. 30–37, 1997.

V. Buldygin, L. Utzet, and V. Zaiats, Asymptotic normality of cross-coorrelogram estimators of the response function, Statistical Infernce for Stochastic Processes, vol. 7, pp. 1–34, 2004.

V. Buldygin, L. Utzet, and V. Zaiats, A note on the application of intergals involving cyclic products of kernels, QESTIIO, vol. 26, no. 1-2, pp. 3—14, 2002.

A. Erdelyi, Higher transcendental functions, Mc Graw-Hill Book Company, Inc, 1953.

I.I. Gikhman, and A.V. Skorokhod, Introduction to the theory of random processes, Dover Publications Inc., Mineola, New York,1996.

E. J. Hannan, and M. Deistler, The Statistical Theory of Linear Systems, Wiley, New York, 1988.

Yu. V. Kozachenko, and O.M. Moklyachuk, Large deviation probabilities for square-Gaussian stochastic processes, Extremes, vol. 2, no. 3, pp. 269–293, 1999.

Yu.V Kozachenko, and O.M. Moklyachuk, Square-Gaussian stochastic processes, Theory of Stoch. Processes, vol. 6(22), no.3-4, pp. 98–121, 2000.

Yu.V. Kozachenko, A.O. Pashko, and I.V. Rozora, Simulation of stochastic processes and fields, Zadruga, Kyiv, 2007. (in Ukrainian)

Yu. Kozacenko, and I. Rozora, On cross-correlogram estimators of impulse response function, Theor. Probability and Math. Statist., vol. 93, pp. 75–83, 2015.

Yu.V. Kozachenko, and O.V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Communications., vol. 3, no. 1, pp. 83–94, 1998.

Yu. Kozachenko, and V. Troshki, A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process, Modern Stochastics: Theory and Applications, vol. 1, no. 1, pp. 139–149, 2014.

M. Schetzen, The Volterra and Wiener Theories of Nonlinear Systems, Wiley, New York, 1980.

T. Soderstr ¨ om, and P. Stoica, ¨ System Identification, Prentice-Hall, London, 1989.

Published
2016-08-30
How to Cite
Rozora, I., & Kozachenko, Y. V. (2016). A Criterion for Testing Hypothesis about Impulse Response Function. Statistics, Optimization & Information Computing, 4(3), 214-232. https://doi.org/10.19139/soic.v4i3.222
Issue
Vol 4 No 3 (2016)
Section
Research Articles
Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).