Optimal rates for independence testing via U-statistic permutation tests

On the Permutation Distribution of Independence Tests

One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman’s coefficient of rank correlation statistic, Fisher-Yates statistic, weighted Mann statistic and others. Under the null hypothesis of independence these test statistics have a permutation distribution th...

I - 1 a Class of Permutation Tests for Stochastic Independence

Bootstrap and permutation tests of independence for point processes

Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general U -statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the u...

Nonparametric Optimal Tests for Independence in the Elliptical VAR Model

In this work we construct a class of locally asymptotically most stringent (in the Le Cam sense) tests for independence between two sets of variables in the VAR models. These tests are based on multivariate ranks of distances and multivariate signs of the observations and are shown to be asymptotically distribution-free under very mild assumptions on the noise, which is obtained by applying a l...

Permutation Tests for Classification

We introduce and explore an approach to estimating statistical significance of classification accuracy, which is particularly useful in scientific applications of machine learning where high dimensionality of the data and the small number of training examples render most standard convergence bounds too loose to yield a meaningful guarantee of the generalization ability of the classifier. Instea...