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On test for checking hypothesis on expectation and covariance function of stochastic process

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Abstract

In this paper, we had constructed the goodness-of-fit tests incorporating several components, like expectation and covariance function, for identification of a non-centered stationary Gaussian stochastic process. For the construction of the corresponding estimators and investigation of their properties we had utilized the theory of Square Gaussian random variables.

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  • Y V Kozachenko
  • T V Hudyvok
  • V B Troshki
  • N V Troshki
Applied methods of statistical modelling. Leningrad: Mashinostroenie
  • A S Shalygin
  • Y I Palagin