Authors: María Alonso Pena, Gerda Claeskens and Irène Gijbels

Abstract: Hyperspherical kernel density estimators (KDE) are studied which use a parametric spherical distribution as a guide. The main benefit is that these estimators improve the bias of non-guided kernel density estimators when the parametric guiding distribution is not too far from the true density, while having the same variance. When using a von Mises Fisher density as a guide, the proposed estimator 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 hyperspheric setting, and is in  contrast to that of similar methods for real-valued data. Moreover, we deal with the important issue of data-driven selection of the concentration parameter. Simulations and real data examples illustrate the finite-sample performance of the proposed method, also in comparison with other recently proposed estimation methods.

Citation: Alonso-Pena, M., Claeskens, G. and Gijbels, I. (2024). Nonparametric estimation of densities on the hypersphere using a parametric guide. To appear in Scandinavian Journal of Statistics.

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