Abstract
A test is proposed for a hypothesis on the correlation function of general Gaussian random processes. The test is based on theorems on estimates of the distribution of the supremum of sample estimators of correlation functions of Gaussian processes. For a wide class of stationary processes formulas are given that allow the test to be used immediately. Bibliography: 4 titles.
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References
Yu. V. Kozachenko and A. I. Stadnik, “On convergence of some functionals of Gaussian vectors in Orlicz spaces,”Teor. Veroyatnost. Mat. Statist.,44, 80–87 (1991).
M. A. Krasnosel’skii and Ya. B. Rutickii,Convex Functions and Orlicz Spaces, Noordhof, Groningen (1961).
Yu. V. Kozachenko and A. I. Stadnik, “Pre-Gaussian processes and convergence inC(T) of estimators of covariance functions,”Teor. Veroyatnost. Mat. Statist.,45, 54–62 (1991).
I. A. Ibragimov and Yu. A. Rozanov,Gaussian Random Processes, Springer-Verlag, Berlin-New York (1970).
Additional information
Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 61–74.
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Kozachenko, Y.V., Kozachenko, L.F. A test for a hypothesis on the correlation function of Gaussian random processes. J Math Sci 77, 3437–3444 (1995). https://doi.org/10.1007/BF02367991
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DOI: https://doi.org/10.1007/BF02367991