Nonparametric adaptive change point estimation and on line detection

Abstract

Rich;tr(lsu~i. Texas 75083-0658 K P~ words and Phrases: CUSUM; gener-ulued likelthood r,atzo. 1rircrr1 delny: m e a n tzme between false alarms; stopping t i~r~~. ABSTRACT Under standard conditions of change-point problems with one or both distributions being unknown, we propose efficient on-line and off-line n o n p a r a~r~r t r i c algorithms for detecting and estimating the change-point. They are based 011 histogram density estimators, which allows applications involving ordinal and categorical data. Also, they are designed to detect any changes in distribution, not necessarily related to the location or scale parameters. EfFicienry of the proposed schemes is demonstrated by relevant inequalities for the rnean delay Downloaded by [Otto-von-Guericke-Universitaet Magdeburg] at 03:36 14 October 2014 2 BARON and the mean time between false alarms. Asymptotically, they are shown to behave similarly t o the most efficient procedures based on the known distributions The stopping rule achieves an asymptotically linear mean delay and an exponential mean time between false alarms. The guidelin~s on selecting the threshold and the partition for the histogram density estimation are given, based on the obtained results. Proposed methods are applied to the England temperatures data and the Vostok ice core record to detect the glol~al climate changes

A new toolkit for robust distributional change detection

“…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.…”

Automatic Identification of Change Points for the System Testing Process

“…This stopping rule achieves asymptotically equivalent mean delay and mean time between false alarms [1].…”

Data Fusion and Type-2 Fuzzy Inference in Contextual Data Stream Monitoring

“…It mainly depends on the signal characteristics and is generally adjusted by experience or by using a training dataset [54]. A number of approaches have been proposed for the definition of h [22], [54], [55], [56], [57], [58], [59], [60], [61]. These efforts handle the research question of automatically defining h through two aspects: (i) theoretical and (ii) application depended.…”

“…These efforts handle the research question of automatically defining h through two aspects: (i) theoretical and (ii) application depended. A few methodologies choose h according to the probability of false alerts and the mean time in the inter-arrivals [55], [56]. The provided formulations are asymptotic and it is difficult to be applied in real scenarios.…”