Detecting Sparse Heterogeneous Mixtures in a Two-Sample Problem

TL;DR

This paper introduces a nonparametric approach using a two-sample higher criticism test to detect sparse heterogeneous mixtures, demonstrating its effectiveness across various sparsity levels compared to the likelihood ratio test.

Contribution

The paper proposes a novel nonparametric higher criticism test for detecting sparse effects in two-sample problems, showing its optimality across all sparsity regimes.

Findings

The higher criticism test is asymptotically comparable to the likelihood ratio test.

The method is effective in all sparsity regimes.

It addresses the detection problem in a nonparametric framework.

Abstract

We consider the problem of detecting sparse heterogeneous mixtures in a two-sample setting from a nonparametric perspective, where the effect manifests itself as a positive shift. We suggest a two-sample higher criticism test, and show that it is first-order comparable to the likelihood ratio test for the generalized Guassian mixture models in all sparsity regimes.