Cross-correlogram estimators of impulse response functions

Authors:
Yu. V. Kozachenko and I. V. Rozora

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **93** (2015).

Journal:
Theor. Probability and Math. Statist. **93** (2016), 79-91

MSC (2010):
Primary 62M20, 60E15

DOI:
https://doi.org/10.1090/tpms/995

Published electronically:
February 7, 2017

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Yu. V. Kozachenko**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine

Email:
yvk@univ.kiev.ua

**I. V. Rozora**

Affiliation:
Department of Applied Statistics, Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine

Email:
irozora@bigmir.net

DOI:
https://doi.org/10.1090/tpms/995

Keywords:
Correlogram,
impulse response function,
large deviation probabilities

Received by editor(s):
July 9, 2015

Published electronically:
February 7, 2017

Additional Notes:
The paper was prepared following the talk at the International Conference “Probability, Reliability and Stochastic Optimization (PRESTO-2015)” held in Kyiv, Ukraine, April 7–10, 2015

Article copyright:
© Copyright 2017
American Mathematical Society