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Robust estimation of location and concentration parameters for the von Mises–Fisher distribution

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  • Shogo Kato
  • Shinto Eguchi

Abstract

Robust estimation of location and concentration parameters for the von Mises–Fisher distribution is discussed. A key reparametrisation is achieved by expressing the two parameters as one vector on the Euclidean space. With this representation, we first show that maximum likelihood estimator for the von Mises–Fisher distribution is not robust in some situations. Then we propose two families of robust estimators which can be derived as minimisers of two density power divergences. The presented families enable us to estimate both location and concentration parameters simultaneously. Some properties of the estimators are explored. Simple iterative algorithms are suggested to find the estimates numerically. It is shown that the presented approaches can be utilised to estimate either the location or concentration parameter. A comparison with the existing robust estimators is given as well as discussion on difference and similarity between the two proposed estimators. A simulation study is made to evaluate finite sample performance of the estimators. We apply the proposed methods to a sea star dataset and discuss the selection of the tuning parameters and outlier detection. Copyright Springer-Verlag Berlin Heidelberg 2016

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  • Shogo Kato & Shinto Eguchi, 2016. "Robust estimation of location and concentration parameters for the von Mises–Fisher distribution," Statistical Papers, Springer, vol. 57(1), pages 205-234, March.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:1:p:205-234
    DOI: 10.1007/s00362-014-0648-9
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    References listed on IDEAS

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    1. J. L. Scealy & A. H. Welsh, 2011. "Regression for compositional data by using distributions defined on the hypersphere," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 351-375, June.
    2. Arnab Laha & K. Mahesh, 2012. "SB-robust estimator for the concentration parameter of circular normal distribution," Statistical Papers, Springer, vol. 53(2), pages 457-467, May.
    3. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    4. Ko, D. J. & Chang, T., 1993. "Robust M-Estimators on Spheres," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 104-136, April.
    5. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    6. Agostinelli, Claudio, 2007. "Robust estimation for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5867-5875, August.
    7. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    8. Jones, M.C. & Pewsey, Arthur, 2005. "A Family of Symmetric Distributions on the Circle," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1422-1428, December.
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    Cited by:

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    3. Luca Greco & Giovanni Saraceno & Claudio Agostinelli, 2021. "Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection," Stats, MDPI, vol. 4(2), pages 1-18, June.
    4. Kirschstein, Thomas & Liebscher, Steffen & Pandolfo, Giuseppe & Porzio, Giovanni C. & Ragozini, Giancarlo, 2019. "On finite-sample robustness of directional location estimators," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 53-75.
    5. Arnab Kumar Laha & A. C. Pravida Raja & K. C. Mahesh, 2019. "SB-robust estimation of mean direction for some new circular distributions," Statistical Papers, Springer, vol. 60(3), pages 877-902, June.

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