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Nonparametric estimation of densities on the hypersphere using a parametric guide

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  • 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
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    References listed on IDEAS

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