Nonparametric measure-transportation-based methods for directional data
基于测度运输的方向数据非参数方法
Abstract This article proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile contours and regions and closed-form formulas under the classical assumption of rotational symmetry. The empirical versions of our distribution functions enjoy the expected Glivenko–Cantelli property of traditional distribution…