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Heterogeneous change point inference.


Munk,  A.
Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society;

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Pein, F., Sieling, H., & Munk, A. (2017). Heterogeneous change point inference. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 79(4), 1207-1227. doi:10.1111/rssb.12202.

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 a, 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.