Theory of Probability and Mathematical Statistics

A criterion for testing hypotheses about the covariance function of a Gaussian stationary process

Author(s): Yu. V. Kozachenko; T. V. Fedoryanych
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 69 (2003).
Journal: Theor. Probability and Math. Statist. No. 69 (2004), 85-94.
MSC (2000): Primary 60G17; Secondary 60G07
Posted: 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.

1.: 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)
2.: 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)
3.: M. A. Krasnosel'ski ${\u{\i}}\kern.15em$ and Ya. B. Ruticki ${\u{\i}}\kern.15em$ , Convex Functions and Orlicz Spaces, Fizmatgiz, Moscow, 1958; English transl., Noordhof, Gröningen, 1961. MR 0106412 (21:5144)

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60G17, 60G07

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: 10.1090/S0094-9000-05-00616-2
PII: S 0094-9000(05)00616-2
Received by editor(s): 19/DEC/2002
Posted: February 8, 2005
Copyright of article: Copyright 2005, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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