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. Yet lack of relevant work has been done regarding structural change detection, including, but not limited to change point identification, profile analysis for piecewise constant coefficients, and integration analysis with multiple data sources. 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. Numerical comparisons with other methods show the superior performance of GKnockoff, in terms of both FDR control and power. We also implement the proposed method to analyze a macroeconomic dataset for detecting change points in the consumer price index, as well as the unemployment rate.

Bio: Jingyuan Liu is Professor from the Department of Statistics in School of Economics and Wang Yanan Institute for Studies in Economics at Xiamen University. 
She obtained her Ph.D. degree in statistics from Penn State at 2013. Her research interests are statistical tools for high and ultrahigh dimensional models,
causal inference, text mining, nonparametric and semi-parametric methods, statistical genetics, and biostatistics.
https://wise.xmu.edu.cn/english/info/1062/1339.htm