LJKProbability & Statistics Seminar

On Thursday September 25 2014 at 14h00 in Noël Gastinel Amphitheater  UFR IMAG F 022

Seminary of Mr Axel MUNK (Université de Goettingen (Allemagne))

Multiscale Change Point Inference

Summary

We introduce a new estimator SMUCE (Simultaneous MUltiscale Changepoint Estimator) for the changepoint problem in exponential family regression. An unknown step function is estimated by minimizing the number of changepoints over the acceptance region of a multiscale test. The probability of overestimating the true number of changepoints 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 nonasymptotic 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.
