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Integrated squared error estimation of Cauchy parameters

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  • Besbeas, Panagiotis
  • Morgan, Byron J. T.
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    Abstract

    We show that integrated squared error estimation of the parameters of a Cauchy distribution, based on the empirical characteristic function, is simple, robust and efficient. The k-L estimator of Koutrouvelis (Biometrika 69 (1982) 205) is more difficult to use, less robust and at best only marginally more efficient.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-44421NW-2/2/976c03ba0a40baa1ca6f4d884484c00d
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 55 (2001)
    Issue (Month): 4 (December)
    Pages: 397-401

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    Handle: RePEc:eee:stapro:v:55:y:2001:i:4:p:397-401

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    Keywords: Cauchy distribution Efficiency Influence function Integrated squared error k-L method Maximum likelihood Robustness;

    References

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    1. Junjiro Ogawa, 1960. "Determination of optimum spacings for the estimation of the scale parameter of an exponential distribution based on sample quantiles," Annals of the Institute of Statistical Mathematics, Springer, vol. 12(2), pages 135-141, June.
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    Cited by:
    1. Muneya Matsui & Akimichi Takemura, 2005. "Goodness-of-Fit Tests for Symmetric Stable Distributions - Empirical Characteristic Function Approach," CIRJE F-Series CIRJE-F-384, CIRJE, Faculty of Economics, University of Tokyo.
    2. Besbeas, Panagiotis & Morgan, Byron J. T., 2004. "Integrated squared error estimation of normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 44(3), pages 517-526, January.
    3. Michael Rockinger & Maria Semenova, 2005. "Estimation of Jump-Diffusion Process vis Empirical Characteristic Function," FAME Research Paper Series rp150, International Center for Financial Asset Management and Engineering.
    4. Muneya Matsui & Akimichi Takemura, 2005. "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(1), pages 183-199, March.
    5. Muneya Matsui & Akimichi Takemura, 2003. "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," CIRJE F-Series CIRJE-F-226, CIRJE, Faculty of Economics, University of Tokyo.
    6. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.

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