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Optimal covariance estimation of discrete-time locally self-similar processes in time-scale and ambiguity domains

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  • Yasaman Maleki

Abstract

This paper investigates the optimal estimate of the covariance function in the sense of mean-square of errors, for the class of discrete-time locally self-similar processes. The covariance function is estimated in time-scale and ambiguity domains. Since the class of estimators is completely characterized in terms of kernels, the problem is reduced to finding the optimal kernel, which is obtained in time-scale domain. Also, the optimal kernel is computed for two classes of discrete-time locally self-similar and locally self-similar chirp processes. Furthermore, it is shown that the proposed method gives more accurate estimate than the ordinary methods for non stationary processes.

Suggested Citation

  • Yasaman Maleki, 2017. "Optimal covariance estimation of discrete-time locally self-similar processes in time-scale and ambiguity domains," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(10), pages 4700-4712, May.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:10:p:4700-4712
    DOI: 10.1080/03610926.2015.1069352
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