A Generalized Knockoff Procedure for FDR Control in Structural Change Detection

TL;DR

This paper introduces a generalized knockoff procedure (GKnockoff) for controlling the false discovery rate in structural change detection, effectively handling high-dimensional data and demonstrating superior performance over existing methods.

Contribution

The paper develops a novel GKnockoff method with proven FDR control, incorporating a screening step for high-dimensional data and applying it to macroeconomic change detection.

Findings

GKnockoff controls FDR exactly in finite samples.

The method outperforms existing approaches in power and FDR control.

Application to macroeconomic data reveals meaningful structural changes.

Abstract

Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there is certainly no shortage of FDR control strategies when selecting individual features, but the relevant works for structural change detection, such as profile analysis for piecewise constant coefficients and integration analysis with multiple data sources, are limited. In this paper, we propose a generalized knockoff procedure (GKnockoff) for FDR control under such problem settings. We prove that the GKnockoff possesses pairwise exchangeability, and is capable of controlling the exact FDR under finite sample sizes. We further explore GKnockoff under high dimensionality, by first introducing a new screening method to filter the high-dimensional potential structural changes. We adopt a data splitting technique to first reduce the dimensionality via screening and then conduct GKnockoff on the refined selection set. Furthermore, the powers of proposed methods are systematically studied. Numerical comparisons with other methods show the superior performance of GKnockoff, in terms of both FDR control and power. We also implement the proposed methods to analyze a macroeconomic dataset for detecting changes of driven effects of economic development on the secondary industry.