论文标题
非参数措施转移的定向数据方法
Nonparametric Measure-Transportation-Based Methods for Directional Data
论文作者
论文摘要
本文提出了基于定向数据的测量运输的各种非参数工具。我们使用最佳传输来定义超出球的新分布和分位功能的新概念，并在经典的旋转对称性假设下具有有意义的分位数轮廓和区域以及封闭形式的公式。我们的分销功能的经验版本享有传统分销功能的预期Glivenko-Cantelli属性。它们提供了排名和标志的完全无分配概念，并定义了（曲线）相似和（超级）子午线的数据驱动系统。基于这一点，我们还构建了对统一性的普遍一致测试，以及一类完全无分配和普遍一致的方向测试，对方向MANOVA进行了测试，在模拟中，这表现优于其所有现有竞争对手。涉及黑子分析的真实数据示例总结了论文。
This paper 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 functions. They provide fully distribution-free concepts of ranks and signs and define data-driven systems of (curvilinear) parallels and (hyper)meridians. Based on this, we also construct a universally consistent test of uniformity and a class of fully distribution-free and universally consistent tests for directional MANOVA which, in simulations, outperform all their existing competitors. A real-data example involving the analysis of sunspots concludes the paper.
