IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i3d10.1007_s00362-016-0853-9.html
   My bibliography  Save this article

SB-robust estimation of mean direction for some new circular distributions

Author

Listed:
  • Arnab Kumar Laha

    (Indian Institute of Management, Ahmedabad)

  • A. C. Pravida Raja

    (Indian Institute of Management, Ahmedabad)

  • K. C. Mahesh

    (Nirma University)

Abstract

The most often used distribution for modelling directional data has been the circular normal (CN) (a.k.a. von-Mises) distribution. Recently Kato and Jones (K–J) introduced a family of distribution which includes the CN distribution as a special case. We study the SB-robustness of the circular mean functional (CMF) and show that the CMF is not SB-robust at the family of all symmetric Kato–Jones distributions but is SB-robust at sub-families with bounded parameters. It is also found to be SB-robust for certain sub-families of wrapped-t (WT) distributions, mixtures of K–J distributions and mixtures of K–J and WT distributions. The SB-robustness of the circular trimmed mean functional (CTMF) is also studied and it is found that the CTMF is SB-robust for larger sub-families of symmetric Kato–Jones distributions compared to that of CMF. The SB-robustness of the CMF for asymmetric families of distributions is studied and it is shown that CMF is SB-robust at a sub-family of asymmetric Kato–Jones distributions. The performance of CTM is compared with that of circular mean (CM) through extensive simulation. It is seen that CTM has better robustness properties than the CM both theoretically and practically. Some guidelines for choice of trimming proportion for CTM is given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:3:d:10.1007_s00362-016-0853-9
    DOI: 10.1007/s00362-016-0853-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0853-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0853-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gill, Jeff & Hangartner, Dominik, 2010. "Circular Data in Political Science and How to Handle It," Political Analysis, Cambridge University Press, vol. 18(3), pages 316-336, July.
    2. 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.
    3. 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.
    4. Stigler, Stephen M., 2010. "The Changing History of Robustness," The American Statistician, American Statistical Association, vol. 64(4), pages 277-281.
    5. Ichiro Ken Shimatani & Ken Yoda & Nobuhiro Katsumata & Katsufumi Sato, 2012. "Toward the Quantification of a Conceptual Framework for Movement Ecology Using Circular Statistical Modeling," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-13, November.
    6. Sungsu Kim & Ashis SenGupta, 2013. "A three-parameter generalized von Mises distribution," Statistical Papers, Springer, vol. 54(3), pages 685-693, August.
    7. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    8. Kato, Shogo & Jones, M. C., 2010. "A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 249-262.
    9. Ko, D. J. & Chang, T., 1993. "Robust M-Estimators on Spheres," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 104-136, April.
    10. Umbach, Dale & Jammalamadaka, S. Rao, 2009. "Building asymmetry into circular distributions," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 659-663, March.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    3. Mojtaba Hatami & Mohammad Hossein Alamatsaz, 2019. "Skew-symmetric circular distributions and their structural properties," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(4), pages 953-969, December.
    4. 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.
    5. Toshihiro Abe & Arthur Pewsey & Kunio Shimizu, 2013. "Extending circular distributions through transformation of argument," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 833-858, October.
    6. Masanobu Taniguchi & Shogo Kato & Hiroaki Ogata & Arthur Pewsey, 2020. "Models for circular data from time series spectra," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 808-829, November.
    7. M. C. Jones & Arthur Pewsey, 2012. "Inverse Batschelet Distributions for Circular Data," Biometrics, The International Biometric Society, vol. 68(1), pages 183-193, March.
    8. Abe, Toshihiro & Miyata, Yoichi & Shiohama, Takayuki, 2023. "Bayesian estimation for mode and anti-mode preserving circular distributions," Econometrics and Statistics, Elsevier, vol. 27(C), pages 136-160.
    9. 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.
    10. Christophe Ley & Thomas Verdebout, 2014. "Skew-rotsymmetric Distributions on Unit Spheres and Related Efficient Inferential Proceedures," Working Papers ECARES ECARES 2014-46, ULB -- Universite Libre de Bruxelles.
    11. Yoichi Miyata & Takayuki Shiohama & Toshihiro Abe, 2023. "Identifiability of Asymmetric Circular and Cylindrical Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1431-1451, August.
    12. Garnett P. McMillan & Timothy E. Hanson & Gabrielle Saunders & Frederick J. Gallun, 2013. "A two-component circular regression model for repeated measures auditory localization data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 515-534, August.
    13. Abe, Toshihiro & Pewsey, Arthur, 2011. "Symmetric circular models through duplication and cosine perturbation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3271-3282, December.
    14. Thomas Dietrich & Wolf-Dieter Richter, 2017. "Classes of Geometrically Generalized Von Mises Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 21-59, May.
    15. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    16. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    17. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    18. Toshihiro Abe & Hiroaki Ogata & Takayuki Shiohama & Hiroyuki Taniai, 2017. "Circular autocorrelation of stationary circular Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 275-290, October.
    19. Giovanni Saraceno & Claudio Agostinelli & Luca Greco, 2021. "Robust estimation for multivariate wrapped models," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 225-240, August.
    20. Xiaoping Zhan & Tiefeng Ma & Shuangzhe Liu & Kunio Shimizu, 2019. "On circular correlation for data on the torus," Statistical Papers, Springer, vol. 60(6), pages 1827-1847, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:60:y:2019:i:3:d:10.1007_s00362-016-0853-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.