We discuss generalized linear models for directional data where the conditional distribution of the response is a von Mises-Fisher distribution in arbitrary dimension or a Bingham distribution on the unit circle. To do this properly, we parametrize von Mises-Fisher distributions by Euclidean parameters and investigate computational aspects of this parametrization. Then we modify this approach for local polynomial regression as a means of nonparametric smoothing of distributional data. The methods are illustrated with simulated data and a data set from planetary sciences involving covariate vectors on a sphere with axial response.

翻译：本文探讨了方向数据的广义线性模型，其中响应变量的条件分布为任意维度下的冯·米塞斯-费舍尔分布或单位圆上的宾汉分布。为实现这一目标，我们采用欧几里得参数对冯·米塞斯-费舍尔分布进行参数化，并研究该参数化的计算特性。随后，我们将此方法拓展至局部多项式回归，作为分布数据非参数平滑的手段。通过模拟数据及行星科学中的球面协变量向量与轴向响应数据集，对所述方法进行了实证演示。