A Scan Procedure for Multiple Testing

TL;DR

This paper introduces a novel scan procedure for multiple testing that scans all intervals to control false discovery rate and potentially improves power over traditional methods like Benjamini-Hochberg.

Contribution

The paper proposes a new scan-based method for multiple testing that offers strong asymptotic FDR control and better power in certain models, extending existing approaches.

Findings

The scan procedure controls asymptotic FDR effectively.

It outperforms Benjamini-Hochberg in power-law models.

Provides conditions where the new method is superior.

Abstract

In a multiple testing framework, we propose a method that identifies the interval with the highest estimated false discovery rate of P-values and rejects the corresponding null hypotheses. Unlike the Benjamini-Hochberg method, which does the same but over intervals with an endpoint at the origin, the new procedure `scans' all intervals. In parallel with \citep*{storey2004strong}, we show that this scan procedure provides strong control of asymptotic false discovery rate. In addition, we investigate its asymptotic false non-discovery rate, deriving conditions under which it outperforms the Benjamini-Hochberg procedure. For example, the scan procedure is superior in power-law location models.