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On robust stopping times for detecting changes in distribution

Golubev, Yuri; Safarian, Mher

Let X1, X2, independent random variables observed sequen-tially and such that X1,...,X θ−1 have a common probability density p 0, while X θ ,X θ +1,...are all distributed according to p 1 6 = p 0. It is assumed that p 0 and p 1 are known, but the time change θ ∈ Z + is unknown and the goal is to construct a stopping time τ that detects the hange-point θ as soon as possible. The existing approaches to this problem rely essentially on some a priori information about θ. For in-stance, in Bayes approaches, it is assumed that θ is a random variable with a known probability distribution. In methods related to hypothesis testing, this a priori information is hidden in the so-called verage run length. The main goal in this paper is to construct stopping times which do not make use of a priorinformation about θ, but have nearly Bayesian detection delays. More precisely, we propose stopping times solving approximately the following problem: ∆ (θ;τα) → min τα subject to α (θ;τα) ≤ α for any θ ≥ 1, where α (θ; τ ) =
P θ { τ < θ} is the false alarm probability and ∆(θ;τ) = E θ (τ−θ) + is the average detection delay, and explai ... mehr

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DOI: 10.5445/IR/1000083279
Veröffentlicht am 06.06.2018
Zugehörige Institution(en) am KIT Institut für Volkswirtschaftslehre (ECON)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2190-9806
KITopen-ID: 1000083279
Verlag KIT, Karlsruhe
Umfang 19 S.
Serie Working paper series in economics ; 116
Schlagworte stopping time, false alarm probability, average detection delay, Bayes stopping time, CUSUM method, multiple hypothesis test- ing
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