Comparison theorems and asymptotic behavior of correlation estimators in spaces of continuous functions. II
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This paper is the second part of . Using the comparison theorems which were proved in the first part, the asymptotic normality of the estimator — in a model of a series of several samples — of the correlation function of a stationary Gaussian random process in spaces of continuous functions with weights is established. A method for constructing functional confidence intervals for an unknown correlation function in these spaces is described.
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- 12.V. V. Buldygin and V. V. Zayats, “Comparison theorems and the asymptotic behavior of correlation estimators in spaces of continuous functions. I,” Ukr. Mat. Zh.,43, No. 4, 482–489 (1991).Google Scholar
- 13.R. E. Maiboroda, “An estimator of the moment generating function of a random variable from the results of observations,” Teor. Veroyatn. Mat. Statist.,32, 121–131 (1985) [English translation,32, 141–151 (1986)].Google Scholar
- 14.I. K. Matsak, Local Properties of Sample Functions of Random Processes, Abstract of Candidate of Phys.-Math. Sciences' Dissertation, Kiev (1977).Google Scholar
- 15.V. V. Zayats, “Application of comparison theorems to a problem of mathematical statistics,” in: Analiticheskie metody issledovaniya evolutsii stokhasticheskikh sistem (Analytic Methods for Investigating the Evolution of Stochastic Systems), Inst. Mat. Akad. Nauk Ukr SSR, Kiev (1989), pp. 30–39.Google Scholar