Title: Stein's Method of Moments on the Sphere Show Chinese title

Title: 球面上的Stein方法矩量

Abstract: We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads to explicit estimators which have good asymptotic properties (close to efficiency) and therefore lead to interesting alternatives to classical maximum likelihood methods or more recent score matching estimators. We perform competitive simulation studies to assess the quality of the new estimators. Finally, the practical relevance of our estimators is illustrated on a real data application in spherical latent representations of handwritten numbers. Show Chinese abstract

Abstract: 我们使用Stein特征来获得三个经典球面分布（即Fisher-Bingham分布、von Mises-Fisher分布和Watson分布）参数的新矩型估计量，在独立同分布的情况下。这导致了具有良好渐近性质（接近效率）的显式估计量，因此为经典的最大似然方法或最近的得分匹配估计量提供了有趣的替代方案。我们进行了竞争性模拟研究以评估新估计量的质量。最后，我们的估计量在手写数字的球面潜在表示的真实数据应用中得到了实际相关性的说明。