Robust selection of the number of change-points via FDR control

Robust quantification of uncertainty regarding the number of change-points presents a significant challenge in data analysis, particularly when employing false discovery rate (FDR) control techniques. Emphasizing the detection of genuine signals while controlling false positives is crucial, especially for identifying shifts in location parameters within flexible distributions. Traditional parametric methods often exhibit sensitivity to outliers and heavy-tailed data. Addressing this limitation, a robust method accommodating diverse data structures is proposed. The approach constructs component-wise sign-based statistics. Leveraging the global symmetry inherent in these statistics enables the derivation of data-driven thresholds suitable for multiple testing scenarios. Method development occurs within the framework of U-statistics, which naturally encompasses existing cumulative sum-based procedures. Theoretical guarantees establish FDR control for the component-wise sign-based method under mild assumptions. Demonstrations of effectiveness utilize simulations with synthetic data and analyses of real data.