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Nonparametric estimation of directional highest density regions

Author

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  • Paula Saavedra-Nieves

    (Universidade de Santiago de Compostela)

  • Rosa M. Crujeiras

    (Universidade de Santiago de Compostela)

Abstract

Highest density regions (HDRs) are defined as level sets containing sample points of relatively high density. Although Euclidean HDR estimation from a random sample, generated from the underlying density, has been widely considered in the statistical literature, this problem has not been contemplated for directional data yet. In this work, directional HDRs are formally defined and plug-in estimators based on kernel smoothing and associated confidence regions are proposed. We also provide a new suitable bootstrap bandwidth selector for plug-in HDRs estimation based on the minimization of an error criteria that involves the Hausdorff distance between the boundaries of the theoretical and estimated HDRs. An extensive simulation study shows the performance of the resulting estimator for the circle and for the sphere. The methodology is applied to analyze two real data sets in animal orientation and seismology.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:3:d:10.1007_s11634-021-00457-4
    DOI: 10.1007/s11634-021-00457-4
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    References listed on IDEAS

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    2. 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).
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    Cited by:

    1. Stanislav Nagy & Houyem Demni & Davide Buttarazzi & Giovanni C. Porzio, 2024. "Theory of angular depth for classification of directional data," 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. 18(3), pages 627-662, September.
    2. Anna Montin & Alessandra R. Brazzale & Giovanna Menardi & Andrea Sottosanti, 2024. "Locating $$\gamma$$ γ -ray sources on the celestial sphere via modal clustering," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(1), pages 153-172, March.

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