A criterion for testing hypotheses about the covariance function of a Gaussian stationary process
Authors:
Yu. V. Kozachenko and T. V. Fedoryanych
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 69 (2004), 85-94
MSC (2000):
Primary 60G17; Secondary 60G07
DOI:
https://doi.org/10.1090/S0094-9000-05-00616-2
Published electronically:
February 8, 2005
MathSciNet review:
2110907
Full-text PDF Free Access
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Abstract: New upper and lower bounds for distributions of quadratic forms of Gaussian random variables as well as those for the limits of quadratic forms are found in this paper. Based on these estimates, a criterion is proposed to test a hypothesis about the covariance function $\rho (\tau )$ of a Gaussian stochastic process.
References
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
- Yurij V. Kozachenko and Olexander V. Stus, Square-Gaussian random processes and estimators of covariance functions, Math. Commun. 3 (1998), no. 1, 83–94 (English, with English and Croatian summaries). MR 1648867
- M. A. Krasnosel′skiĭ and Ja. B. Rutickiĭ, Vypuklye funktsii i prostranstva Orlicha, Problems of Contemporary Mathematics, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958 (Russian). MR 0106412
References
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, TViMS, Kiev, 1998; English transl., AMS, Providence, 2000. MR 1743716 (2001g:60089)
- Yu. V. Kozachenko and O. V. Stus, Square Gaussian random processes and estimator of covariance functions, Math. Commun. 3 (1998), no. 1, 83–94. MR 1648867 (2000b:60099)
- M. A. Krasnosel’skiĭ and Ya. B. Rutickiĭ, Convex Functions and Orlicz Spaces, Fizmatgiz, Moscow, 1958; English transl., Noordhof, Gröningen, 1961. MR 0106412 (21:5144)
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Additional Information
Yu. V. Kozachenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Glushkova 6, Kyiv 03127, Ukraine
Email:
yvk\@univ.kiev.ua
T. V. Fedoryanych
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Glushkova 6, Kyiv 03127, Ukraine
Email:
fedoryanich\@univ.kiev.ua
Received by editor(s):
December 19, 2002
Published electronically:
February 8, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
