Change-Point Detection Under Dependence Based on Two-Sample U-Statistics

Dehling, Herold; Fried, Roland; García, Isabel Cristina Gil; Wendler, Martin

doi:10.1007/978-1-4939-3076-0_12

Cited by 30 publications

(53 citation statements)

References 34 publications

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“…In addition, many deterministic dynamical systems such as expanding maps of the unit interval are covered as well. Dehling et al (2013a) have studied the asymptotic distribution of the two-sample U-statistics process in the case of SRD noise, extending results obtained earlier by Csörgő and Horváth (1988) in the case of IID noise. Under some technical conditions, concerning the β-mixing coefficients and the continuity of f and h, and under the null hypothesis of no change, we could show that…”

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Comments on: Extensions of some classical methods in change point analysis

Dehling

2014

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First of all, I would like to compliment the authors for writing this very fine survey paper on some recent developments in change-point analysis. There is a lot of current research activity devoted to change-point analysis, and many articles have appeared since the publication of the seminal book by Csörgő and Horváth (1997). Among the topics covered in the present paper are empirical process techniques, Darling-Erdős laws, changes in correlations, changes in regression parameters, sequential testing, panel models, and functional data. Horváth and Rice provide an excellent survey of some of the recent results, which will be helpful to all researchers in this area.In my discussion, I will complement the paper by Horváth and Rice by presenting some recent results on U-statistics-based robust change-point tests for time series. In a series of papers, see Dehling and Fried (2012), Dehling et al. (2013aDehling et al. ( , 2013bDehling et al. ( , 2013c and Betken (2014), we have investigated such tests and derived their asymptotic distribution, both in the case of short-range as well as long-range dependent time series.We consider a model where the data are generated by X i = μ i + i , where μ i is an unknown signal and i is a stationary ergodic noise process with E( i ) = 0. Given the observations X 1 , . . . , X n , we wish to test the hypothesis of no change, i.e. H : μ 1 = · · · = μ n , against the alternative A : μ 1 = · · · = μ k = μ k+1 = · · · = μ n , for some 1 ≤ k ≤ n − 1.This comment refers to the invited paper available at

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“…In a series of papers, see Dehling and Fried (2012), Dehling et al (2013aDehling et al ( , 2013bDehling et al ( , 2013c and Betken (2014), we have investigated such tests and derived their asymptotic distribution, both in the case of short-range as well as long-range dependent time series.…”

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Comments on: Extensions of some classical methods in change point analysis

Dehling

2014

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“…Other existing works that also focus on establishing asymptotic distribution of the detection statistic under the null for controlling the false alarm rate include the following: Harchaoui et al (2008) present a maximum kernel Fisher discriminant ratio statistic and study its asymptotic null distribution; Dehling et al (2015) investigate the two-sample test U -statistic for dependent data. Our approach is different from above in that we focus on directly approximating the tail of the detection statistic under the null, rather than trying to obtain its asymptotic distribution.…”

Section: Related Workmentioning

confidence: 99%

ScanB-statistic for kernel change-point detection

Xie

Dai

et al. 2019

Sequential Analysis

141

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Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been used for this task, which enjoys fewer assumptions on the distributions than the parametric approach and can handle high-dimensional data. In this paper, we focus on the scenario when the amount of background data is large, and propose a computationally efficient kernel-based statistics for change-point detection, which are inspired by the recently developed B-statistics. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using the change-of-measure technique, which focuses on characterizing the tail of the detection statistics rather than obtaining its asymptotic distribution under the null distribution. Such approximations are crucial to controlling the false alarm rate, which corresponds to the average-run-length in online change-point detection. Our approximations are shown to be highly accurate. Thus, they provide a convenient way to find detection thresholds for online cases without the need to resort to the more expensive simulations. We show that our methods perform well on both synthetic data and real data.

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“…We call this the Huberization test, using the sample medianμ n and median absolute deviation about the medianκ n of the data for standardization, and c = 1.5 to achieve a reasonable compromise between performance under normality and under heavy-tails. Dehling et al (2015) construct a Wilcoxon change-point test based on the twosample Wilcoxon-Mann-Whitney statistic. Vogel & Wendler (2017) use the difference between the one-sample Hodges-Lehmann estimators Med{(X i + X j )/2 : i = 1, .…”

Section: Simulation Resultsmentioning

confidence: 99%

“…(ii) For fixed t, the process {U n (λ, t) : 0 ≤ λ ≤ 1} is a two-sample U-process that has been introduced and investigated by Dehling et al (2015).…”

Section: Two-sample Empirical U-quantile Processmentioning

confidence: 99%

A robust method for shift detection in time series

2020

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We present a robust test for a change-point in time series which is based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes, in the case of short range dependent observations. Using this theory we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on Ustatistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so that any transform of the observed process can be used to test the stability of higher order characteristics such as variability, skewness or curtosis.

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Change-Point Detection Under Dependence Based on Two-Sample U-Statistics

Cited by 30 publications

References 34 publications

Comments on: Extensions of some classical methods in change point analysis

Comments on: Extensions of some classical methods in change point analysis

ScanB-statistic for kernel change-point detection

A robust method for shift detection in time series

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