  We propose HSMUCE (heterogeneous simultaneous multiscale change-point
estimator) 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 in order to keep a
global nominal level alpha, even for finite samples. We show that HSMUCE
controls the error of over- and underestimation of the number of change-points.
To this end, 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. HSMUCE 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 HSMUCE 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 online.
