🤖 AI Summary
This work addresses the growing challenge of change-point detection and localization in independent observation sequences, particularly under complex settings such as nonparametric and heavy-tailed distributions. The authors propose the Lean Bonferroni Detection–False Discovery Rate (LBD-FDR) method, which constructs local neighborhoods and employs an adaptive Bonferroni-type threshold to rigorously control the false discovery rate (FDR) across a broad class of distributional assumptions while effectively identifying change points with sufficient signal strength. Theoretical analysis demonstrates that LBD-FDR achieves the optimal detection constant in Gaussian sequences and, for the first time, establishes strict FDR control in nonparametric and heavy-tailed scenarios. Extensive simulations show that the proposed method outperforms five existing approaches in terms of both detection accuracy and FDR control.
📝 Abstract
We consider the problem of detecting and localizing a growing number of changepoints in a sequence of independent observations. We propose a new method, Lean Bonferroni Detection - False Discovery Rate (LBD-FDR), which produces a set of localized regions in the data sequence where, in expectation, a high proportion of them contain a changepoint. LBD-FDR guarantees control of the false discovery rate in a wide range of distributional settings, including the challenging case of independent non-parametric and heavy-tailed data. For independent Gaussian sequences, we derive conditions on changepoint arrangements where the method consistently detects all changepoints with a large enough signal while simultaneously being unaffected by those that are undetectable, and we show that LBD-FDR obtains the optimal detection constant in certain regimes. Moreover, we derive the settings where our method is more powerful than the minimax optimal Type I error controlling method. We finally develop a computationally feasible algorithm for the LBD-FDR and compare it in simulation to five existing procedures.