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Integrated squared error estimation of Cauchy parameters

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

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.

Suggested Citation

  • Besbeas, Panagiotis & Morgan, Byron J. T., 2001. "Integrated squared error estimation of Cauchy parameters," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 397-401, December.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:4:p:397-401
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    References listed on IDEAS

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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;The Institute of Statistical Mathematics, vol. 12(2), pages 135-141, June.
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    Cited by:

    1. 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.
    2. 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;The Institute of Statistical Mathematics, vol. 57(1), pages 183-199, March.
    3. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
    4. Besbeas, Panagiotis & J.T. Morgan, Byron, 2004. "Efficient and robust estimation for the one-sided stable distribution of index," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 251-257, February.
    5. 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.
    6. 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.
    7. 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.
    8. Yuichi Akaoka & Kazuki Okamura & Yoshiki Otobe, 2022. "Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 895-923, October.

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