Heterogeneous change point inference

By Florian Pein, Hannes Sieling, Axel Munk. 2015

89 citations recorded by the source corpus.

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 α, 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.

Subfields: Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8e2360d137d091e59ea18cd61355991a65380022

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In Molecular Biology

1. Nicolas Vayatis
2. Laurent Oudre
3. Charles Truong

In Statistics and Probability

1. Nicolas Vayatis
2. Laurent Oudre
3. Charles Truong

Citations in the corpus

• Selective review of offline change point detection methods (2020, methodology): “Historically, the Gaussian distribution was first used, to model 269 mean-shifts [52–54] and scale shifts [39, 50, 55].”
• A review of change point detection methods (2018, methodology): “tions must be known before performing the detection, usually thanks to prior knowledge on the data. Historically, the Gaussian distribution was rst used, to model mean-shifts [52{54] and scale shifts [39, 50, 55]. A large part of the literature then evolved towards other parametric distributions, mo”