Theory of Probability and Mathematical Statistics

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

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.

References:

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)

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