IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v153y2019icp90-97.html
   My bibliography  Save this article

Non-subjective priors for wrapped Cauchy distributions

Author

Listed:
  • Ghosh, Malay
  • Zhong, Xiaolong
  • SenGupta, Ashis
  • Zhang, Ruoyang

Abstract

Circular data can arise from many sources, such as image processing, protein structure, and geological data, just to name a few. Wrapped stable family of distributions constitute one of the most widely used class of distributions for the analysis of such data. Wrapped Cauchy distribution is a member of this family and it is the only one known to have a single term explicit pdf compared to the infinite series representations for all the others. We develop in this paper reference priors and probability matching priors for this distribution, which turn out to be quite elegant and provide good frequentist performance as well.

Suggested Citation

  • Ghosh, Malay & Zhong, Xiaolong & SenGupta, Ashis & Zhang, Ruoyang, 2019. "Non-subjective priors for wrapped Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 90-97.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:90-97
    DOI: 10.1016/j.spl.2019.05.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219301452
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.05.016?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. Shogo Kato & Arthur Pewsey, 2015. "A Möbius transformation-induced distribution on the torus," Biometrika, Biometrika Trust, vol. 102(2), pages 359-370.
    2. G. Datta & J. Ghosh, 1995. "Noninformative priors for maximal invariant parameter in group models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 95-114, June.
    3. 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.
    4. Abe, Toshihiro & Ley, Christophe, 2017. "A tractable, parsimonious and flexible model for cylindrical data, with applications," Econometrics and Statistics, Elsevier, vol. 4(C), pages 91-104.
    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. 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.
    3. 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.
    4. Imoto, Tomoaki & Abe, Toshihiro, 2021. "Simple construction of a toroidal distribution from independent circular distributions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    5. 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.
    6. Gugliani, G.K. & Sarkar, A. & Ley, C. & Mandal, S., 2018. "New methods to assess wind resources in terms of wind speed, load, power and direction," Renewable Energy, Elsevier, vol. 129(PA), pages 168-182.
    7. Andrew Harvey & Dario Palumbo, 2023. "Regime switching models for circular and linear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 374-392, July.
    8. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    9. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.
    10. 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.
    11. Ventura, Laura & Sartori, Nicola & Racugno, Walter, 2013. "Objective Bayesian higher-order asymptotics in models with nuisance parameters," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 90-96.
    12. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2013. "Non-parametric Regression for Circular Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 238-255, June.
    13. 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.
    14. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    15. 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.
    16. M. C. Jones & Arthur Pewsey, 2012. "Inverse Batschelet Distributions for Circular Data," Biometrics, The International Biometric Society, vol. 68(1), pages 183-193, March.
    17. Kociecki, Andrzej, 2012. "Orbital Priors for Time-Series Models," MPRA Paper 42804, University Library of Munich, Germany.
    18. Fangpo Wang & Alan E. Gelfand, 2014. "Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1565-1580, December.
    19. 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.
    20. 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.

    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:eee:stapro:v:153:y:2019:i:c:p:90-97. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.