Change-point detection in multinomial data using phi-divergence test statistics

Batsidis, Apostolos; Horváth, Lajos; Martín, Nirian; Pardo, Leonardo; Zografos, K.

doi:10.1016/j.jmva.2013.03.008

Cited by 16 publications

(11 citation statements)

References 7 publications

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“…Moreover, Qahtan et al rely on

\max false{D_{ϕ_{1}}^{C A S} false(P_{1, N_{1}}^{normale normalm normalp, s m o}, P_{2, N_{2}}^{normale normalm normalp, s m o} false), D_{ϕ_{1}}^{C A S} false(P_{2, N_{2}}^{normale normalm normalp, s m o}, P_{1, N_{1}}^{normale normalm normalp, s m o} false) false}

. Batsidis et al basically use certain maxima over bunches of divergences of the form

D_{ϕ}^{C A S} false(P_{1, N_{1}}^{normale normalm normalp}, \frac{N_{1}}{N_{1} + N_{2}} \cdot P_{1, N_{1}}^{normale normalm normalp} + \frac{N_{2}}{N_{1} + N_{2}} \cdot P_{2, N_{2}}^{normale normalm normalp} false)

where they build on earlier results of Horváth and Serbinowska for the case ϕ ( t ) = ϕ 2 (·) (see also the work of Baron for similar investigations with ϕ = ϕ 1 (·)). In contrast, Batsidis et al and Martín and Pardo work with certain maxima over bunches of divergences of the form

D_{ϕ}^{C A S} false(P_{1}^{{\overset{θ}{true}}_{1, N_{1}}}, P_{2}^{{\overset{θ}{true}}_{2, N_{2}}} false)

with maximum likelihood parameter estimators

{\overset{θ}{true}}_{1, N_{1}}

\overset{θ}{true}

…”

Section: The Divergence Frameworkmentioning

confidence: 99%

“…Some detection investigations along this line have been done in the abovementioned works. [35][36][37][38][39][40][41][42][43][44] To add more flexibility (eg, toward better robustness properties, cf Section 4), we extend the abovementioned toolkit to {D ,M (P 1,N 1 , P 2,N 2 ) ∶ ∈ , M ∈ }, where  is a set of possibly adaptive ( -finite) scaling measures.…”

Section: Example 1 (A)mentioning

confidence: 99%

“…In a different approach, Qahtan et al rely on the symmetric robust maximum of the KL divergence and the reversed KL divergence. For the detection of change points in multinomial data, Batsidis et al use the maximum of Csiszár‐Ali‐Silvey ϕ ‐divergences between certain pairs of empirical distributions in subsamples; for their investigations, they rely on the corresponding earlier results in the work of Horváth et al for the special case of the Pearson chi‐square divergence (see also the work of Baron for similar investigations based on the KL divergence). Along the same lines with Csiszár‐Ali‐Silvey ϕ ‐divergences, Batsidis et al, Martín and Pardo analyze the case of general parametric distributions.…”

Section: Introductionmentioning

confidence: 99%

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A new toolkit for robust distributional change detection

Kißlinger

Stummer

2018

Appl Stoch Models Bus & Ind

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Divergences (distances), which measure the dissimilarity, respectively, proximity, between two probability distributions, have turned out to be very useful for several different tasks in statistics (eg, parameter estimation and goodness‐of‐fit testing), econometrics, machine learning, information theory, etc. Some prominent examples are the Kullback‐Leibler information (relative entropy), the Csiszár‐Ali‐Silvey ϕ‐divergences, the “ordinary” (ie, unscaled) Bregman divergences, and the recently developed more general scaled Bregman divergences. Out of the latter and a novel extension to nonconvex generators, we form a new toolkit for detecting distributional changes in random data (streams and clouds). Some sample‐size asymptotics is investigated as well.

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“…Moreover, Qahtan et al rely on

\max false{D_{ϕ_{1}}^{C A S} false(P_{1, N_{1}}^{normale normalm normalp, s m o}, P_{2, N_{2}}^{normale normalm normalp, s m o} false), D_{ϕ_{1}}^{C A S} false(P_{2, N_{2}}^{normale normalm normalp, s m o}, P_{1, N_{1}}^{normale normalm normalp, s m o} false) false}

. Batsidis et al basically use certain maxima over bunches of divergences of the form

D_{ϕ}^{C A S} false(P_{1, N_{1}}^{normale normalm normalp}, \frac{N_{1}}{N_{1} + N_{2}} \cdot P_{1, N_{1}}^{normale normalm normalp} + \frac{N_{2}}{N_{1} + N_{2}} \cdot P_{2, N_{2}}^{normale normalm normalp} false)

D_{ϕ}^{C A S} false(P_{1}^{{\overset{θ}{true}}_{1, N_{1}}}, P_{2}^{{\overset{θ}{true}}_{2, N_{2}}} false)

with maximum likelihood parameter estimators

{\overset{θ}{true}}_{1, N_{1}}

\overset{θ}{true}

…”

Section: The Divergence Frameworkmentioning

confidence: 99%

Section: Example 1 (A)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new toolkit for robust distributional change detection

Kißlinger

Stummer

2018

Appl Stoch Models Bus & Ind

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“…The authors speak about several methods proposed in Batsidis et al (2013) to detect changes in multinomial data based on divergence test statistics but the domain of application of divergence test statistics to detect changes goes far beyond that of multinomial data because divergence test statistics can be used for testing parameter changes in general models. In i.i.d.…”

mentioning

confidence: 99%

“…Based on the results of Batsidis et al (2013Batsidis et al ( , 2014, it would be possible to consider general families (in the sense that these families would have as a particular case the empirical likelihood ratio test) of empirical divergence test statistics to solve different problems related to the change-point analysis.…”

mentioning

confidence: 99%

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

Martín

Pardo

2014

TEST

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Professor Horváth co-authored in 1997 the book entitled "Limit theorems in changepoint analysis". It can be seen as a milestone in the history of this topic that has a history of over 50 years. This review paper is very interesting, timely, highly informative and provides a comprehensive summary of the recent research on change-point analysis. This research has deserved considerable attention during the last years and is expected to develop new results in the near future. Professors Horváth and Rice are to be congratulated for this succinct and insightful presentation of the state-of-art of the change-point methodology. The review not only considers the most frequently used classical methods and ideas in change-point analysis but also some new methodology developed in the last years in relation to time series, multivariate, panel data and functional data. The applications of several classical results to real data sets permit us a better understanding as well as showing the importance and scope of this theory that was originated in the 1940s but is currently an active area of research. It is an almost an impossible task to review the very extensive literature on change-point analysis in a single paper. Nevertheless, the paper contains a very rich collection of the contributions not only from the classical results but also from the most recent papers in change-point analysis. We want to thank professors Horváth and Rice for their enormous effort in bringing us all this existing material on a topic of the highest relevance.This comment refers to the invited paper available at

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