Heterogeneous change point inference

• 成果类型: Article
• 署名作者: Pein, Florian; Sieling, Hannes; Munk, Axel
• 署名单位: University of Gottingen; Max Planck Society
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12202
• 发表日期: 2017
• 页码: 1207-1227
• 关键词: multiscale inference; binary segmentation; nuisance parameter; linear-models; computation; number; noise; scan

摘要

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.