Ukrainian Mathematical Journal

, Volume 43, Issue 5, pp 535–539 | Cite as

Comparison theorems and asymptotic behavior of correlation estimators in spaces of continuous functions. II

  • V. V. Buldygin
  • V. V. Zayats
Article

Abstract

This paper is the second part of [12]. 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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Literature cited

  1. 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
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    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
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    I. K. Matsak, Local Properties of Sample Functions of Random Processes, Abstract of Candidate of Phys.-Math. Sciences' Dissertation, Kiev (1977).Google Scholar
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    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

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • V. V. Buldygin
    • 1
    • 2
  • V. V. Zayats
    • 1
    • 2
  1. 1.Kiev Polytechnical InstituteUSSR
  2. 2.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRKiev

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