Multiscale Change Point Inference
Séminaire Probabilités & Statistique
25/09/2014 - 14:00 Mr Axel MUNK (Université de Goettingen (Allemagne)) Amphithéâtre Bernard Vauquois - UFR IMAG F 018
We introduce a new estimator SMUCE (Simultaneous MUltiscale Change-point Estimator) for the change-point problem in exponential family regression. An unknown step function is estimated by minimizing the number of change-points over the acceptance region of a multiscale test. The probability of overestimating the true number of change-points K is controlled by the asymptotic null distribution of the multiscale test statistic. Further, we derive exponential bounds for the probability of underestimating K. Balancing these quantities allows to maximize the probability of correctly estimating K. All results are non-asymptotic for the normal case. Based on these bounds, we construct honest confidence sets for the unknown step function and its change- points. It is shown that SMUCE asymptotically achieves the optimal detection rate of vanishing signals in a multiscale setting. Several extensions are discussed, such as FDR based thresholding. We illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions. The performance of the proposed multiscale approach is illustrated by simulations and in several applications including ion channel recordings, CGH array analysis, and photoemission spectroscopy.