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On the trace approximations of products of Toeplitz matrices

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  • Ginovyan, Mamikon S.
  • Sahakyan, Artur A.

Abstract

The paper establishes error orders for integral limit approximations to the traces of products of Toeplitz matrices generated by integrable real symmetric functions defined on the unit circle. These approximations and the corresponding error bounds are of importance in the statistical analysis of discrete-time stationary processes: asymptotic distributions and large deviations of Toeplitz type random quadratic forms, estimation of the spectral parameters and functionals, etc.

Suggested Citation

  • Ginovyan, Mamikon S. & Sahakyan, Artur A., 2013. "On the trace approximations of products of Toeplitz matrices," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 753-760.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:753-760
    DOI: 10.1016/j.spl.2012.11.019
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    References listed on IDEAS

    as
    1. Offer Lieberman & Peter C. B. Phillips, 2004. "Error bounds and asymptotic expansions for toeplitz product functionals of unbounded spectra," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 733-753, September.
    2. Bercu, B. & Gamboa, F. & Rouault, A., 1997. "Large deviations for quadratic forms of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 75-90, October.
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