Multiple change-point estimation with U-statistics

Döring, Maik

doi:10.1016/j.jspi.2010.01.040

Cited by 14 publications

(3 citation statements)

References 11 publications

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“…There is extensive literature that covers changes in expectation, e.g., methods based on likelihood ratios (Gombay and Horváth, 1994;Fang et al, 2020), empirical processes (Horváth and Shao, 2007;Holmes et al, 2013), U -statistics (Gombay and Horváth, 2002;Horváth and Hušková, 2005;Döring, 2010), least-squares (Lavielle and Moulines, 2000;Harchaoui and Lévy-Leduc, 2010) and many more. We mention methodology based * corresponding author on CUSUM-statistics, e.g., by Page (1954); Hinkley (1971); Berkes et al (2006); Dehling et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Multiscale change point detection via gradual bandwidth adjustment in moving sum processes

Levajković¹,

Messer²

2021

Preprint

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A method for the detection of changes in the expectation in univariate sequences is provided. Moving sum processes are studied. These rely on the selection of a tuning bandwidth. Here, a framework to overcome bandwidth selection is presented -the bandwidth adjusts gradually. For that, moving sum processes are made dependent on both time and the bandwidth: the domain becomes a triangle. On the triangle, paths are constructed which systematically lead to change points. An algorithm is provided that estimates change points by subsequent consideration of paths. Strong consistency for the number and location of change points is shown. Simulations support estimation precision. A companion R-package mscp is made available on CRAN.

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Section: Introductionmentioning

confidence: 99%

Multiscale change point detection via gradual bandwidth adjustment in moving sum processes

Levajković¹,

Messer²

2021

Preprint

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“…Most of the change detection strategies are based mainly either on estimation or on testing. Non-exhaustive references on estimation approaches are [6], [23], [24], [17], [4], [2], [37] and [66]. Some references on testing approaches are, among others, [45], [15], [20], [21], [63], [28], [5], [68], [27], [43], [26] and [31].…”

Section: Introductionmentioning

confidence: 99%

On detecting weak changes in the mean of CHARN models

Ngatchou-Wandji¹,

Ltaifa²

2021

Preprint

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We study a likelihood ratio test for detecting multiple weak changes in the mean of a class of CHARN models. The locally asymptotically normal (LAN) structure of the family of likelihoods under study is established. It results that the test is asymptotically optimal and an explicit form of its asymptotic local power is given as a function of candidates change locations. Weak changes locations estimates are obtained as the time indexes maximizing an estimate of the local power. A simulation study shows the good performance of our methods compared to some CUSUM approaches. Our results are also applied to three sets of real data.

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“…This motivated Csörgő and Horváth [3] to study more general U -statistics for change point detection, followed by Ferger [9] and Gombay [11]. Orasch [17] and Döring [8] have studied U -statistics for detecting multiple change-points in a sequence of independent observations. Results for change point tests based on general two-sample U -statistics for short range dependent time series were given by Dehling, Fried, Garcia, Wendler [5], for long range dependent time series by Dehling, Rooch, Wendler [7].…”

Section: Introductionmentioning

confidence: 99%

Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment

Račkauskas

Wendler

2020

Stat Papers

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To detect a changed segment (so called epedimic changes) in a time series, variants of the CUSUM statistic are frequently used. However, they are sensitive to outliers in the data and do not perform well for heavy tailed data, especially when short segments get a high weight in the test statistic. We will present a robust test statistic for epidemic changes based on the Wilcoxon statstic. To study their asymptotic behavior, we prove functional limit theorems for U -processes in Hölder spaces. We also study the finite sample behavior via simulations and apply the statistics to a real data example.If the changed segment is rather short compared to the sample size, tests who give higher weight to short segments have more power. Asymptotic critical values for such tests have been proved by Sigmund [23] in Gaussian case (see also [22]). The logarithmic case was treated in Kabluchko and Wang [14], whereas the regular varying case in Mikosch and Račkauskas [16]. Yao [26] and Hušková [12] compared tests with different wheightings. Račkauskas and Suquet [20], [21] have suggested to use a compromise weighting, that allows to express the limit distribution of the test statistic as a function of a Brownian motion. However, in order to apply the continuous mapping theorem for this statistic, it is necessary to establish the weak convergence of the partial sum process to a Brownian motion with respect to the Hölder norm.It is well known that the CUSUM statistic is sensitive to outliers in the data, see e.g. Prášková and Chochola [19]. The problem becomes worse if higher weights are given to shorter segments. A common strategy to obtain a robust change point test is to adapt robust two-sample test like the Wilcoxon one. This was first used by Darkhovsky [4] and by Pettitt [18] in the context of detecting at most one change in a sequence of independent observations. For a comparison of different change point test see Wolfe and Schechtmann [25]. The results on the Wilcoxon type change point statistic were generalized to long range dependent time series by Dehling, Rooch, Taqqu [6]. The Wilcoxon statistic can either be expressed as a rank statistic or as a (two-sample) U -statistic. This motivated Csörgő and Horváth [3] to study more general U -statistics for change point detection, followed by Ferger [9] and Gombay [11]. Orasch [17] and Döring [8] have studied U -statistics for detecting multiple change-points in a sequence of independent observations. Results for change point tests based on general two-sample U -statistics for short range dependent time series were given by Dehling, Fried, Garcia, Wendler [5], for long range dependent time series by Dehling, Rooch, Wendler [7].Gombay [10] has suggested to use a Wilcoxon type test also for the epidemic change problem. The aim of this paper is to generalize these results in three aspects: to study more general U -statistics, to allow the random variable to exhibit some form of short range dependence, and to introduce weightings to the statistic. This way, we obtain a robust test...

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Multiple change-point estimation with U-statistics

Cited by 14 publications

References 11 publications

Multiscale change point detection via gradual bandwidth adjustment in moving sum processes

Multiscale change point detection via gradual bandwidth adjustment in moving sum processes

On detecting weak changes in the mean of CHARN models

Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment

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