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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 85-94
MSC (2000): Primary 60G17; Secondary 60G07
Published electronically: February 8, 2005
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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.


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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: yvkuniv.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: fedoryanichuniv.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00616-2
PII: S 0094-9000(05)00616-2
Received by editor(s): December 19, 2002
Published electronically: February 8, 2005
Article copyright: © Copyright 2005 American Mathematical Society