标题： 适用于高维数据的精确分布无关的球对称性检验 显示英文标题

标题： Exact distribution-free tests of spherical symmetry applicable to high dimensional data

摘要： 我们基于数据增强的方法开发了一些基于图的检验方法来检验多元分布的球面对称性。 这些检验方法是通过沿一条路径计算的新概念下的符号和秩得到的，该路径是通过对增广数据集中观测值之间的成对不相似性优化一个目标函数获得的。 基于这些符号和秩构造的检验具有确切的分布自由性质，并且无论数据维数如何，检验统计量的零分布保持不变。 这些检验可以方便地用于高维数据，即使维数远大于样本量。 在适当的正则性条件下，我们在高维渐近框架下证明了这些检验的一致性，其中维度趋于无穷大，而样本量可能或可能不随维度增长。 我们还提出了方法的一种推广，以处理零假设未指定对称中心的情况。 分析了几个模拟数据集和一个真实数据集，以展示所提出检验方法的实用性。 显示英文摘要

摘要： We develop some graph-based tests for spherical symmetry of a multivariate distribution using a method based on data augmentation. These tests are constructed using a new notion of signs and ranks that are computed along a path obtained by optimizing an objective function based on pairwise dissimilarities among the observations in the augmented data set. The resulting tests based on these signs and ranks have the exact distribution-free property, and irrespective of the dimension of the data, the null distributions of the test statistics remain the same. These tests can be conveniently used for high-dimensional data, even when the dimension is much larger than the sample size. Under appropriate regularity conditions, we prove the consistency of these tests in high dimensional asymptotic regime, where the dimension grows to infinity while the sample size may or may not grow with the dimension. We also propose a generalization of our methods to take care of the situations, where the center of symmetry is not specified by the null hypothesis. Several simulated data sets and a real data set are analyzed to demonstrate the utility of the proposed tests.