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M-estimator-based robust estimation of the number of components of a superimposed sinusoidal signal model

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  • Sharmishtha Mitra
  • Amit Mitra

Abstract

In this paper, we consider the problem of estimating the number of components of a superimposed nonlinear sinusoids model of a signal in the presence of additive noise. We propose and provide a detailed empirical comparison of robust methods for estimation of the number of components. The proposed methods, which are robust modifications of the commonly used information theoretic criteria, are based on various M-estimator approaches and are robust with respect to outliers present in the data and heavy-tailed noise. The proposed methods are compared with the usual non-robust methods through extensive simulations under varied model scenarios. We also present real signal analysis of two speech signals to show the usefulness of the proposed methodology.

Suggested Citation

  • Sharmishtha Mitra & Amit Mitra, 2014. "M-estimator-based robust estimation of the number of components of a superimposed sinusoidal signal model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 853-878, April.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:4:p:853-878
    DOI: 10.1080/02664763.2013.856387
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    1. Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(3), pages 478-493, June.
    2. Ronchetti, Elvezio, 1985. "Robust model selection in regression," Statistics & Probability Letters, Elsevier, vol. 3(1), pages 21-23, February.
    3. Muller, Samuel & Welsh, A.H., 2005. "Outlier Robust Model Selection in Linear Regression," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1297-1310, December.
    4. Wu, Tiee-Jian & Sepulveda, Alfred, 1998. "The weighted average information criterion for order selection in time series and regression models," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 1-10, July.
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