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Determination of Discrete Spectrum in a Random Field

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  • Debasis Kundu
  • Swagata Nandi

Abstract

We consider a two dimensional frequency model in a random field, which can be used to model textures and also has wide applications in Statistical Signal Processing. First we consider the usual least squares estimators and obtain the consistency and the asymptotic distribution of the least squares estimators. Next we consider an estimator, which can be obtained by maximizing the periodogram function. It is observed that the least squares estimators and the estimators obtained by maximizing the periodogram function are asymptotically equivalent. Some numerical experiments are performed to see how the results work for finite samples. We apply our results on simulated textures to observe how the different estimators perform in estimating the true textures from a noisy data.

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  • Debasis Kundu & Swagata Nandi, 2003. "Determination of Discrete Spectrum in a Random Field," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(2), pages 258-284, May.
    • Handle: RePEc:bla:stanee:v:57:y:2003:i:2:p:258-284
    DOI: 10.1111/1467-9574.00230
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    Cited by:

    1. Grover, Rhythm & Kundu, Debasis & Mitra, Amit, 2018. "Approximate least squares estimators of a two-dimensional chirp model and their asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 211-220.
    2. Debasis Kundu & Swagata Nandi, 2021. "On Chirp and Some Related Signals Analysis: A Brief Review and Some New Results," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 844-890, August.

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