Multiscale change point inference

By K. Frick, Axel Munk, Hannes Sieling. 2013

368 citations recorded by the source corpus.

We introduce a new estimator, the simultaneous multiscale change point estimator SMUCE, 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 at a level α. 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. By balancing these quantities, α will be chosen such that the probability of correctly estimating K is maximized. All results are even non‐asymptotic for the normal case. On the basis of these bounds, we construct (asymptotically) honest confidence sets for the unknown step function and its change points. At the same time, we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate O(n−1) up to a log‐term. Finally, the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n→∞, even for an unbounded number of change points. We illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions. The performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy.

Subfields: Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0c89185bdc81860e762304a15da399ffd7744994

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Citations in the corpus

A review of change point detection methods (2018, background): “It has been applied for instance on DNA array data [50], geology signals [33].”
Exact post-selection inference for the generalized lasso path (2018, background): “[12], who develop a simultaneous confidence band for the mean in a changepoint model.”
Finite sample change point inference and identification for high‐dimensional mean vectors (2017, methodology): “The current paper uses CUSUM statistics for fixed sampled size tests, as in many other statistical change point testing and estimation works (Aue et al., 2009; Bai, 1997; Berkes et al., 2009; Bhattacharya, 1987; Brodsky & Darkhovsky, 1993; Carlstein, 1988; Csörgo ̋ & Horváth, 1997; Frick et al., 20”
Univariate mean change point detection: Penalization, CUSUM and optimality (2018, methodology): “• There exist several results and algorithms for change point detection using l0 penalization, including Liebscher and Winkler (1999), Friedrich et al. (2008), Boysen et al. (2009) and Killick et al.”
Detecting relevant changes in time series models (2014, methodology): “One obvious idea is to use binary segmentation methods for this problem (see for example Cho and Fryzlewicz (2015)), but multiscale inference (see Frick et al. (2014)) or methods based on spectral analysis (see for example Preuss et al. (2014)) might yield to other powerful methods.”
Heterogeneous change point inference (2015, methodology): “This is optimal in the sense that no signal with a smaller rate can be detected asymptotically with probability 1 (see Dümbgen and Spokoiny (2001), Chan and Walther (2013) and Frick et al. (2014)) for the case of homogeneous observations, and note that this is a submodel of our model.”
Selective review of offline change point detection methods (2020, methodology): “This cost function is also referred to as the quadratic 301 error loss and has been applied for instance on DNA array data [15] and 302 geology signals [6].”
A MOSUM procedure for the estimation of multiple random change points (2018, methodology): “Precisely, the methods are: Segmentor from the Segmentor3IsBack-R-Package, CumSeg as described in [34], SMUCE as described in [18] as well as PELT as described in [23].”