On false discovery control under dependence

TL;DR

This paper extends false discovery control methods to models where null hypotheses are dependent, providing asymptotic theory for false discovery proportions under spatial dependence.

Contribution

It introduces a conditional dependence model for null hypotheses, generalizing the independent assumption in false discovery control.

Findings

Asymptotic properties of false discovery proportions are derived.

Large-sample distributional theory is established.

Dependence structure helps characterize spatial null hypothesis patterns.

Abstract

A popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent. This paper generalizes the random effects model to a conditional dependence model which allows dependence between null hypotheses. The dependence can be useful to characterize the spatial structure of the null hypotheses. Asymptotic properties of false discovery proportions and numbers of rejected hypotheses are explored and a large-sample distributional theory is obtained.