DeepAI AI Chat
Log In Sign Up

Detection of Sparse Positive Dependence

by   Ery Arias-Castro, et al.

In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main component. We first look at this problem in the context of a normal mixture model. In essence, the situation reduces to a univariate setting where the effect is a decrease in variance. In particular, a higher criticism test based on the pairwise differences is shown to achieve the detection boundary defined by the (oracle) likelihood ratio test. We then turn to a Gaussian copula model where the marginal distributions are unknown. Standard invariance considerations lead us to consider rank tests. In fact, a higher criticism test based on the pairwise rank differences achieves the detection boundary in the normal mixture model, although not in the very sparse regime. We do not know of any rank test that has any power in that regime.


page 1

page 2

page 3

page 4


Signal detection via Phi-divergences for general mixtures

In this paper we are interested in testing whether there are any signals...

Detecting Sparse Heterogeneous Mixtures in a Two-Sample Problem

We consider the problem of detecting sparse heterogeneous mixtures in a ...

Detection of Sparse Mixtures: Higher Criticism and Scan Statistic

We consider the problem of detecting a sparse mixture as studied by Ings...

The Sparse Variance Contamination Model

We consider a Gaussian contamination (i.e., mixture) model where the con...

Gaussian approximation of Gaussian scale mixture

For a given positive random variable V>0 and a given Z∼ N(0,1) independe...

Learning Sparse Mixture Models

This work approximates high-dimensional density functions with an ANOVA-...

Inference of Microbial Interactions Using Copula Models with Mixture Margins

Quantification of microbial interactions from 16S rRNA and meta-genomic ...