Simultaneous Jump Detection for Multiple Sequences via Screening and Multiple Testing
Shengji Jia, Chunming Zhang · Statistica Sinica · 2025
The estimation of nonparametric discontinuous regression function is fundamental in many applied fields, but challenges arise when the number of jumps (or discontinuities) is large and unknown.We propose a new jump detection method, via the consecutive screening and multiple testing (SaMT) algorithm, for simultaneously estimating the unknown number of jump points and detecting their locations in the flexible nonparametric regression model, guaranteeing the desired accuracy.The initial jump candidates are obtained in the consecutive screening procedure combined with locally-linear smoothing method.To further assess the significance of an individual jump candidate, we develop a novel test based on profile likelihood inference.The ultimate selection of relevant jump points is conducted in a multiple testing procedure, which eliminates irrelevant jump points with large variations, due to heteroscedastic errors, from jump candidates.Moreover, we generalize the SaMT algorithm to detect common jump points shared across multiple aligned sequences.The proposed method is easy