Optimal rank-based tests for homogeneity of scatter

Optimal rank-based testing for principal components

This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudo-Gaussian robustifications by Davis (1977) and Tyler (1981, 1983). The rank-based tests address a much broader class of problems, where covariance matrices need not exist and principal components are associated with more general scatter matrices. The proposed tests are shown to outperform daily practice both from the point of view of validity as fr…

On the Discrete Cramér-von Mises Statistics under Random Censorship

In this work, nonparametric log-rank-type statistical tests are introduced in order to verify homogeneity of purely discrete variables subject to arbitrary right-censoring for infinitely many categories. In particular, the Cramér-von Mises test statistics for discrete models under censoring is established. In order to introduce the test, we develop the weighted log-rank statistics in a general multivariate discrete setup which complements previous fundamental results of Gill (1980) and Andersen et al. (1982). Due to the presence of persistent jumps over the unbounded set of categories, the asy…

一种基于点间距离上平均Wilcoxon秩和的两样本检验

A two-sample test based on averaged Wilcoxon rank sums over interpoint distances

针对点云降维生成的距离样本存在依赖性的问题，提出基于平均Wilcoxon秩和的两样本多元同质性检验，证明其渐近性质与一致性，给出方差近似实现无分布检验，经模拟验证在高维小样本下性能良好，并应用于遗传微阵列病例对照研究。

High Dimensional Spatial Rank Test for Two-Sample Location Problem

This article concerns tests for the two-sample location problem when the dimension is larger than the sample size. The traditional multivariate-rank-based procedures cannot be used in high dimensional settings because the sample scatter matrix is not available. We propose a novel high-dimensional spatial rank test in this article. The asymptotic normality is established. We can allow the dimension being almost the exponential rate of the sample sizes. Simulations demonstrate that it is very robust and efficient in a wide range of distributions.

A One-Sample Test for Normality with Kernel Methods

We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test data for normality or to test parameters (mean and covariance) if data are assumed Gaussian. Our test is based on the same principle as the MMD (Maximum Mean Discrepancy) which is usually used for two-sample tests such as homogeneity or independence testing. Our method makes use of a special kind of parametric bootstrap (typical of goodness-of-fit tests) which …