Change-point testing for parallel data sets with FDR control

Large parallel data sets—consisting of paired measurements of responses and covariates—collected over time from numerous sources are ubiquitous. It is of great interest to identify the data sources where the underlying regression relationship of each data set has shifted. To be specific, the regression coefficient is changed to another one at some time point for each data set. Borrowing the strength of recent developments of multiple testing procedures, a residual-aggregated testing (RAT) method is proposed for recovering such data sources by controlling the false discovery rate (FDR). The proposed method can effectively incorporate the dependence structure among different data sets, and is more robust than the conventional Benjamini-Hochberg method based on asymptotic p-values or numerical approximations. Under mild conditions, the asymptotic validity for both the false discovery proportion and FDR control is established. Extensive numerical results further confirm the effectiveness and robustness of the proposed method.