IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i8p1046-1051.html
   My bibliography  Save this article

Frame theory in directional statistics

Author

Listed:
  • Ehler, Martin
  • Galanis, Jennifer

Abstract

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. To predict these distributions, we merge directional statistics with frame theory and find that probabilistic tight frames yield non-uniform distributions that minimize directional potentials, leading to failure of uniformity rejection for the Bingham test. Finally, we apply our results to model patterns found in granular rod experiments.

Suggested Citation

  • Ehler, Martin & Galanis, Jennifer, 2011. "Frame theory in directional statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1046-1051, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1046-1051
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211000733
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Rueda, Cristina & Fernández, Miguel A. & Peddada, Shyamal Das, 2009. "Estimation of Parameters Subject to Order Restrictions on a Circle With Application to Estimation of Phase Angles of Cell Cycle Genes," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 338-347.
    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.
    2. Tobias Springer & Katja Ickstadt & Joachim Stöckler, 2011. "Frame potential minimization for clustering short time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 341-355, December.

    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. Matthijs J. Warrens & Bunga C. Pratiwi, 2016. "Kappa Coefficients for Circular Classifications," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 507-522, October.
    2. Barragán, Sandra & Fernández, Miguel & Rueda, Cristina & Peddada, Shyamal, 2013. "isocir: An R Package for Constrained Inference Using Isotonic Regression for Circular Data, with an Application to Cell Biology," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i04).
    3. Cristina Rueda & Miguel A. Fernández & Sandra Barragán & Kanti V. Mardia & Shyamal D. Peddada, 2016. "Circular piecewise regression with applications to cell‐cycle data," Biometrics, The International Biometric Society, vol. 72(4), pages 1266-1274, December.
    4. Nuñez-Antonio, Gabriel & Gutiérrez-Peña, Eduardo, 2014. "A Bayesian model for longitudinal circular data based on the projected normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 506-519.
    5. Conde, David & Fernández, Miguel & Salvador, Bonifacio & Rueda, Cristina, 2015. "dawai: An R Package for Discriminant Analysis with Additional Information," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i10).

    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:81:y:2011:i:8:p:1046-1051. 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.