A comprehensive exploration of complete cross-validation for circular data

Kamila  Hasilová; Ivana Horová; David Vališ; Stanislav Zámecník

doi:https://doi.org/10.59170/stattrans-2024-024

A comprehensive exploration of complete cross-validation for circular data

Kamila Hasilová Department of Quantitative Methods, Faculty of Military Leadership, University of Defence, Brno, Czech Republic ORCID:https://orcid.org/0000-0003-1540-3489 , Ivana Horová Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic , David Vališ Department of Combat and Special Vehicles, Faculty of Military Technology, University of Defence, Brno, Czech Republic , Stanislav Zámecník Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic Statistics in Transition new series, vol. 25, 2024, 3, pages: 1-12 Published online: 4 September 2024 https://doi.org/10.59170/stattrans-2024-024 Citation: Hasilová K., Horová I., Vališ D., Zámecník S., 2024. A comprehensive exploration of complete cross-validation for circular data. Statistics in Transition new series, 25(3), pp. 1-12. https://doi.org/10.59170/stattrans-2024-024

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ABSTRACT

Kernel density estimation of circular data has recently received considerable attention for its ability to model and analyse distributions on unit circles and other periodic domains. Our aim is to contribute to the literature on data-driven bandwidth selectors in circular kernel density estimation. We propose a novel circular-specific method that is based on a crossvalidation procedure with a von Mises density used as a kernel function. Using simulated data as well as real-world circular datasets, we evaluate and validate the proposed method and compare it with the existing methods.

KEYWORDS

circular data, kernel density estimation, von Mises density, cross-validation method.

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