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A criterion for testing hypotheses about the covariance function of a Gaussian stationary process. (Ukrainian, English) Zbl 1097.62077
Teor. Jmovirn. Mat. Stat. 69, 79-88 (2004); translation in Theory Probab. Math. Stat. 69, 85-94 (2004).
The authors investigate properties of the space of square-Gaussian random variables. They propose new upper and lower bounds for distributions of quadratic forms of Gaussian random variables as well as those for limits of quadratic forms. These estimates are used to construct a criterion to test a hypothesis about the covariance function \(\rho(\tau)\) of a Gaussian stochastic process \(\xi(t)\) based on the estimate \(\hat\rho(\tau)= T^{-1} \int^T_0\xi(\tau+t)\xi(t)dt\). The constructed estimates are more precise than the ones proposed by V. V. Buldygin and Yu. V. Kozachenko [Metric characterization of random variables and random processes. Translations of Mathematical Monographs. 188, 257 p. (2000; Zbl 0998.60503)].

MSC:
62M07 Non-Markovian processes: hypothesis testing
60G15 Gaussian processes
60G10 Stationary stochastic processes
62M02 Markov processes: hypothesis testing
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