IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v80y2018i1d10.1007_s13171-018-0144-8.html
   My bibliography  Save this article

Statistical Shape Methodology for the Analysis of Helices

Author

Listed:
  • Mai F. Alfahad

    (University of Leeds)

  • John T. Kent

    (University of Leeds)

  • Kanti V. Mardia

    (University of Leeds
    University of Oxford)

Abstract

Consider a helix in three-dimensional space along which a sequence of equally spaced points is observed, subject to statistical noise. For data coming from a single helix, a two-stage algorithm based on a profile likelihood is developed to compute the maximum likelihood estimate of the helix parameters. Statistical properties of the estimator are studied and comparisons are made to other estimators found in the literature. Next a likelihood ratio test is developed to test if there is a change point in the helix, splitting the data into two sub-helices. The shapes of protein α-helices are used to illustrate the methodology.

Suggested Citation

  • Mai F. Alfahad & John T. Kent & Kanti V. Mardia, 2018. "Statistical Shape Methodology for the Analysis of Helices," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 8-32, December.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-018-0144-8
    DOI: 10.1007/s13171-018-0144-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-018-0144-8
    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/s13171-018-0144-8?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. K. V. Mardia, 1999. "Estimation of torsion," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 373-381.
    2. Kanti V. Mardia & Karthik Sriram & Charlotte M. Deane, 2018. "A statistical model for helices with applications," Biometrics, The International Biometric Society, vol. 74(3), pages 845-854, September.
    3. Kanti V. Mardia, 2013. "Statistical approaches to three key challenges in protein structural bioinformatics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 487-514, May.
    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. Kanti V. Mardia, 2021. "Comments on: 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 59-63, 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. Kanti V. Mardia, 2021. "Comments on: 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 59-63, March.
    2. Kanti V. Mardia & Karthik Sriram & Charlotte M. Deane, 2018. "A statistical model for helices with applications," Biometrics, The International Biometric Society, vol. 74(3), pages 845-854, September.
    3. Mardia, Kanti V. & Wiechers, Henrik & Eltzner, Benjamin & Huckemann, Stephan F., 2022. "Principal component analysis and clustering on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. M. Jones & Arthur Pewsey & Shogo Kato, 2015. "On a class of circulas: copulas for circular distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 843-862, October.
    5. Fernández-Durán Juan José & Gregorio-Domínguez MarÍa Mercedes, 2014. "Modeling angles in proteins and circular genomes using multivariate angular distributions based on multiple nonnegative trigonometric sums," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 1-18, February.
    6. Yukari Shirota & Takako Hashimoto, 2017. "Visual Explanation of Deformation Theories in Shape Analysis," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 54(1), pages 1-12.
    7. Catur Apriono & Riti Fitri Sari & Yuriko Yano & Yukari Shirota, 2017. "Economic Indicator Evaluation Based on Shape Deformation Analysis of Indonesian Provinces Statistics," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 54(3), pages 185-206.

    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:sankha:v:80:y:2018:i:1:d:10.1007_s13171-018-0144-8. 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.