Heterogeneous change point inference

Summary

We propose, a heterogeneous simultaneous multiscale change point estimator called ‘H‐SMUCE’ for the detection of multiple change points of the signal in a heterogeneous Gaussian regression model. A piecewise constant function is estimated by minimizing the number of change points over the acceptance region of a multiscale test which locally adapts to changes in the variance. The multiscale test is a combination of local likelihood ratio tests which are properly calibrated by scale‐dependent critical values to keep a global nominal level α, even for finite samples. We show that H‐SMUCE controls the error of overestimation and underestimation of the number of change points. For this, new deviation bounds for F‐type statistics are derived. Moreover, we obtain confidence sets for the whole signal. All results are non‐asymptotic and uniform over a large class of heterogeneous change point models. H‐SMUCE is fast to compute, achieves the optimal detection rate and estimates the number of change points at almost optimal accuracy for vanishing signals, while still being robust. We compare H‐SMUCE with several state of the art methods in simulations and analyse current recordings of a transmembrane protein in the bacterial outer membrane with pronounced heterogeneity for its states. An R‐package is available on line.