DeepAI AI Chat
Log In Sign Up

Optimal rates for independence testing via U-statistic permutation tests

by   Thomas B. Berrett, et al.

We study the problem of independence testing given independent and identically distributed pairs taking values in a σ-finite, separable measure space. Defining a natural measure of dependence D(f) as the squared L_2-distance between a joint density f and the product of its marginals, we first show that there is no valid test of independence that is uniformly consistent against alternatives of the form {f: D(f) ≥ρ^2 }. We therefore restrict attention to alternatives that impose additional Sobolev-type smoothness constraints, and define a permutation test based on a basis expansion and a U-statistic estimator of D(f) that we prove is minimax optimal in terms of its separation rates in many instances. Finally, for the case of a Fourier basis on [0,1]^2, we provide an approximation to the power function that offers several additional insights.


page 1

page 2

page 3

page 4


Local permutation tests for conditional independence

In this paper, we investigate local permutation tests for testing condit...

USP: an independence test that improves on Pearson's chi-squared and the G-test

We present the U-Statistic Permutation (USP) test of independence in the...

Nonparametric Independence Testing for Right-Censored Data using Optimal Transport

We propose a nonparametric test of independence, termed OPT-HSIC, betwee...

A test for normality and independence based on characteristic function

In this article we prove a generalization of the Ejsmont characterizatio...

Adaptive Independence Tests with Geo-Topological Transformation

Testing two potentially multivariate variables for statistical dependenc...

Measuring dependence powerfully and equitably

Given a high-dimensional data set we often wish to find the strongest re...

Matroidal Approximations of Independence Systems

Milgrom (2017) has proposed a heuristic for determining a maximum weight...