Nonparametric estimation of densities on the hypersphere using a parametric guide
研究了一种以参数分布为引导的超球面核密度估计方法，在引导模型接近真实密度时能改善偏差，且即使模型错误也表现良好，并解决了平滑参数的数据驱动选择问题。
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.