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Modified sequential change point procedures based on estimating functions

Kirch, Claudia; Weber, Silke

A large class of sequential change point tests are based on estimating functions where estimation is computationally efficient as (possibly numeric) optimization is restricted to an initial estimation. This includes examples as diverse as mean changes, linear or non-linear autoregressive and binary models. While the standard cumulative-sum-detector (CUSUM) has recently been considered in this general setup, we consider several modifications that have faster detection rates in particular if changes do occur late in the monitoring period. More presicely, we use three different types of detector statistics based on partial sums of a monitoring function, namely the modified moving-sum-statistic (mMOSUM), Page’s cumulative-sum-statistic (Page-CUSUM) and the standard moving-sum-statistic (MOSUM). The statistics only differ in the number of observations included in the partial sum. The mMOSUM uses a bandwidth parameter which multiplicatively scales the lower bound of the moving sum. The MOSUM uses a constant bandwidth parameter, while Page-CUSUM chooses the maximum over all possible lower bounds for the partial sums. So far, the first two schemes have only been studied in a linear model, the MOSUM only for a mean change.
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Verlagsausgabe §
DOI: 10.5445/IR/1000084898
Veröffentlicht am 30.07.2018
DOI: 10.1214/18-EJS1431
Zitationen: 5
Web of Science
Zitationen: 4
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 1935-7524
KITopen-ID: 1000084898
Erschienen in Electronic journal of statistics
Verlag Institute of Mathematical Statistics (IMS)
Band 12
Heft 1
Seiten 1579–1613
Nachgewiesen in Scopus
Web of Science
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