IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v30y2021i1d10.1007_s11749-021-00764-0.html
   My bibliography  Save this article

Comments on: Recent advances in directional statistics

Author

Listed:
  • Stephan F. Huckemann

    (Georg-August-Universität Göttingen)

Abstract

Inspired by this felicitous, highly concentrated and rather exhaustive review of a rapidly growing field, many larger research areas that warrant further investigation come to mind. In this comment, three areas are selected: fully satisfactory PCA on tori and polyspheres, harnessing linearity through Lie algebras underlying homogeneous spaces such as those for directional data, and statistical analysis based on critical points (e.g. mode and antimodes) of Fréchet $$L^p$$ L p -functions.

Suggested Citation

  • Stephan F. Huckemann, 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 71-75, March.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:1:d:10.1007_s11749-021-00764-0
    DOI: 10.1007/s11749-021-00764-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-021-00764-0
    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/s11749-021-00764-0?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. Alfred Kume & Ian L. Dryden & Huiling Le, 2007. "Shape-space smoothing splines for planar landmark data," Biometrika, Biometrika Trust, vol. 94(3), pages 513-528.
    2. Sungkyu Jung & Ian L. Dryden & J. S. Marron, 2012. "Analysis of principal nested spheres," Biometrika, Biometrika Trust, vol. 99(3), pages 551-568.
    3. Lizhen Lin & Brian St. Thomas & Hongtu Zhu & David B. Dunson, 2017. "Extrinsic Local Regression on Manifold-Valued Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1261-1273, July.
    4. T. Hotz & S. Huckemann, 2015. "Intrinsic means on the circle: uniqueness, locus and asymptotics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 177-193, February.
    5. Wang, Yunfan & Patrangenaru, Vic & Guo, Ruite, 2020. "A Central Limit Theorem for extrinsic antimeans and estimation of Veronese–Whitney means and antimeans on planar Kendall shape spaces," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    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. 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).

    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. Kwang‐Rae Kim & Ian L. Dryden & Huiling Le & Katie E. Severn, 2021. "Smoothing splines on Riemannian manifolds, with applications to 3D shape space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 108-132, February.
    3. Vic Patrangenaru & Yifang Deng, 2021. "Extrinsic Regression and Anti-Regression on Projective Shape Manifolds," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 629-646, June.
    4. Arthur Pewsey & Eduardo García-Portugués, 2021. "Rejoinder 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 76-82, March.
    5. Ian L. Dryden & Kwang-Rae Kim & Huiling Le, 2019. "Bayesian Linear Size-and-Shape Regression with Applications to Face Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 83-103, February.
    6. Rabi Bhattacharya & Rachel Oliver, 2019. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-36, February.
    7. 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).
    8. Lazar, Drew & Lin, Lizhen, 2017. "Scale and curvature effects in principal geodesic analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 64-82.
    9. Chiara Brombin & Luigi Salmaso & Lara Fontanella & Luigi Ippoliti, 2015. "Nonparametric combination-based tests in dynamic shape analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 460-484, December.
    10. Stefan Sommer, 2019. "An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 37-62, February.
    11. Ruite Guo & Hwiyoung Lee & Vic Patrangenaru, 2023. "Test for Homogeneity of Random Objects on Manifolds with Applications to Biological Shape Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1178-1204, August.
    12. J. Derek Tucker & Drew Yarger, 2024. "Elastic functional changepoint detection of climate impacts from localized sources," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    13. M. Moghimbeygi & M. Golalizadeh, 2017. "Longitudinal shape analysis by using the spherical coordinates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1282-1295, May.
    14. Yannis Pantazis & Michail Tsagris & Andrew T. A. Wood, 2019. "Gaussian Asymptotic Limits for the α-transformation in the Analysis of Compositional Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 63-82, February.
    15. Victor M. Panaretos & Tung Pham & Zhigang Yao, 2014. "Principal Flows," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 424-436, March.
    16. Xiongtao Dai & Zhenhua Lin & Hans‐Georg Müller, 2021. "Modeling sparse longitudinal data on Riemannian manifolds," Biometrics, The International Biometric Society, vol. 77(4), pages 1328-1341, December.
    17. Meisam Moghimbeygi & Mousa Golalizadeh, 2019. "A longitudinal model for shapes through triangulation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 99-121, March.
    18. Fraiman, Ricardo & Gamboa, Fabrice & Moreno, Leonardo, 2019. "Connecting pairwise geodesic spheres by depth: DCOPS," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 81-94.
    19. Tucker, J. Derek & Wu, Wei & Srivastava, Anuj, 2013. "Generative models for functional data using phase and amplitude separation," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 50-66.
    20. Georgios I. Papayiannis & Stelios Psarakis & Athanasios N. Yannacopoulos, 2023. "Modelling of Functional Profiles and Explainable Shape Shifts Detection: An Approach Combining the Notion of the Fréchet Mean with the Shape-Invariant Model," Mathematics, MDPI, vol. 11(21), pages 1-24, October.

    More about this item

    Keywords

    Primary 62H11; Secondary 62H25;

    JEL classification:

    Statistics

    Access and download statistics

    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:testjl:v:30:y:2021:i:1:d:10.1007_s11749-021-00764-0. 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.