The choice of bandwidth is crucial in circular kernel density estimation. Various bandwidth selection techniques have been proposed in the literature. New bandwidth selectors based on the measure \(\beta \)-divergence for kernel density estimation with circular data are presented in this work. These selectors are obtained by minimizing the mean of the measure \(\beta \)-divergence between the density to be estimated and its estimator. The idea is based on the generalization of the standard method which selects the bandwidth by minimizing the mean integrated squared error (MISE). The performance of the proposed selectors is evaluated through a simulation study and compared with other existing selectors. These selectors are illustrated with some real datasets.

带宽的选择在圆核密度估计中至关重要。文献中已经提出了各种带宽选择技术。这项工作提出了基于圆形数据核密度估计的测量\(\beta \)散度的新带宽选择器。这些选择器是通过最小化要估计的密度与其估计器之间的测量\(\beta \)散度的平均值来获得的。该想法基于标准方法的推广，该方法通过最小化均方误差 (MISE) 来选择带宽。通过模拟研究评估所提出的选择器的性能，并与其他现有选择器进行比较。这些选择器用一些真实的数据集进行说明。