IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v51y2024i3p956-986.html

Nonparametric estimation of densities on the hypersphere using a parametric guide

Author

Listed:
  • María Alonso‐Pena
  • Gerda Claeskens
  • Irène Gijbels

Abstract

Hyperspherical kernel density estimators (KDE), which use a parametric distribution as a guide, are studied in this paper. The main benefit is that these estimators improve the bias of nonguided kernel density estimators when the parametric guiding distribution is not too far from the true density, while preserving the variance. When using a von Mises‐Fisher density as guide, the proposal performs as well as the classical KDE, even when the guiding model is incorrect, and far from the true distribution. This benefit is particular for the hyperspherical setting given its compact support, and is in contrast to similar methods for real valued data. Moreover, we deal with the important issue of data‐driven selection of the smoothing parameter. Simulations and real data examples illustrate the finite‐sample performance of the proposed method, also in comparison with other recently proposed estimation methods.

Suggested Citation

  • María Alonso‐Pena & Gerda Claeskens & Irène Gijbels, 2024. "Nonparametric estimation of densities on the hypersphere using a parametric guide," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 956-986, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:956-986
    DOI: 10.1111/sjos.12737
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12737
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12737?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
    ---><---

    References listed on IDEAS

    as
    1. Eduardo García-Portugués & Davy Paindaveine & Thomas Verdebout, 2020. "On Optimal Tests for Rotational Symmetry Against New Classes of Hyperspherical Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1873-1887, December.
    2. Talamakrouni, Majda & Van Keilegom, Ingrid & El Ghouch, Anouar, 2016. "Parametrically guided nonparametric density and hazard estimation with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 308-323.
    3. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
    4. Tsuruta, Yasuhito & Sagae, Masahiko, 2017. "Higher order kernel density estimation on the circle," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 46-50.
    5. Taylor, Charles C., 2008. "Automatic bandwidth selection for circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3493-3500, March.
    6. Young Kyung Lee & Enno Mammen & Byeong U. Park, 2023. "Hilbertian additive regression with parametric help," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 35(3), pages 622-641, July.
    7. Xu, Danli & Wang, Yong, 2023. "Density estimation for spherical data using nonparametric mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    8. Talamakrouni, Majda & Van Keilegom, Ingrid & El Ghouch, Anouar, 2016. "Parametrically guided nonparametric density and hazard estimation with censored data," LIDAM Reprints ISBA 2016001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Bai, Z. D. & Rao, C. Radhakrishna & Zhao, L. C., 1988. "Kernel estimators of density function of directional data," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 24-39, October.
    10. Di Marzio, Marco & Panzera, Agnese & Taylor, Charles C., 2009. "Local polynomial regression for circular predictors," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2066-2075, October.
    11. Glad, Ingrid K., 1998. "A note on unconditional properties of a parametrically guided Nadaraya-Watson estimator," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 101-108, January.
    12. Graciela Boente & Daniela Rodriguez & Wenceslao González Manteiga, 2014. "Goodness-of-fit Test for Directional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 259-275, March.
    Full references (including those not matched with items on IDEAS)

    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. Tsuruta, Yasuhito, 2024. "Bias correction for kernel density estimation with spherical data," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    3. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," 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. 16(3), pages 761-796, September.
    4. Stanislav Zámečník & Ivana Horová & Stanislav Katina & Kamila Hasilová, 2024. "An adaptive method for bandwidth selection in circular kernel density estimation," Computational Statistics, Springer, vol. 39(4), pages 1709-1728, June.
    5. 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.
    6. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.
    7. Pham Ngoc, Thanh Mai, 2019. "Adaptive optimal kernel density estimation for directional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 248-267.
    8. Aboubacar Amiri & Baba Thiam & Thomas Verdebout, 2017. "On the Estimation of the Density of a Directional Data Stream," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 249-267, March.
    9. Charles C. Taylor & Kanti V. Mardia & Marco Di Marzio & Agnese Panzera, 2012. "Validating protein structure using kernel density estimates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2379-2388, July.
    10. Eduardo GarcÍa-Portugués & Ingrid Van Keilegom & Rosa M. Crujeiras and & Wenceslao González-Manteiga, 2016. "Testing parametric models in linear-directional regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1178-1191, December.
    11. Moawia Alghalith, 2022. "Methods in Econophysics: Estimating the Probability Density and Volatility," Papers 2301.10178, arXiv.org.
    12. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
    13. Babacar Diakhate & Hamza Dhaker & Papa Ngom, 2024. "The $$\beta $$ β -divergence for Bandwidth Selection in Circular Kernel Density Estimation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(3), pages 417-437, September.
    14. Claudio Durastanti, 2016. "Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 651-673, November.
    15. Di Marzio, Marco & Fensore, Stefania & Panzera, Agnese & Taylor, Charles C., 2019. "Kernel density classification for spherical data," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 23-29.
    16. Yoon, Changwon & Choi, Hyunbin & Ahn, Jeongyoun, 2025. "Kernel density estimation for compositional data with zeros via hypersphere mapping," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).
    17. Jeong Min Jeon & Ingrid Van Keilegom, 2024. "Density estimation and regression analysis on hyperspheres in the presence of measurement error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 513-556, June.
    18. Zihao Wu & Carolina Euan & Rosa M. Crujeiras & Ying Sun, 2023. "Estimation and Clustering of Directional Wave Spectra," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 502-525, September.
    19. Bedouhene Kahina & Zougab Nabil, 2020. "A Bayesian procedure for bandwidth selection in circular kernel density estimation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(1), pages 69-82, March.
    20. Oliveira, María & Crujeiras, Rosa M. & Rodríguez-Casal, Alberto, 2014. "NPCirc: An R Package for Nonparametric Circular Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i09).

    More about this item

    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:bla:scjsta:v:51:y:2024:i:3:p:956-986. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.