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On Toeplitz type quadratic functionals of stationary Gaussian processes
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  • Published: September 1994

On Toeplitz type quadratic functionals of stationary Gaussian processes

  • M. S. Ginovian1 

Probability Theory and Related Fields volume 100, pages 395–406 (1994)Cite this article

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Summary

A central limit theorem for Toeplitz type quadratic functionals of a stationary Gaussian processX(t),t∈ℝ, is proved, generalizing the result of Avram [1] for discrete time processes. The result is applied to the problem of nonparametric estimation of linear functionals of an unknown spectral density function. We give some upper bounds for the minimax mean square risk of the nonparametric estimators, similar to those by Ibragimov and Has'minskii [12] for a probability density function.

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References

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Authors and Affiliations

  1. Institute of Mathematics, Armenian National Academy of Sciences, Bagramian 24-B, 375019, Yerevan, Armenia

    M. S. Ginovian

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  1. M. S. Ginovian
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Ginovian, M.S. On Toeplitz type quadratic functionals of stationary Gaussian processes. Probab. Th. Rel. Fields 100, 395–406 (1994). https://doi.org/10.1007/BF01193706

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  • Received: 13 December 1993

  • Revised: 28 March 1994

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01193706

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Mathematics Subject Classifications (1980)

  • 60F05
  • 60G15
  • 62M15
  • 60G10
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