KIT | KIT-Bibliothek | Impressum | Datenschutz

On robust stopping times for detecting changes in distribution

Golubev, Yuri; Safarian, Mher

Abstract:

Let X1, X2,...be 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 explain why such top-ping times are robust w.r.t. ... mehr


Volltext §
DOI: 10.5445/IR/1000083279
Veröffentlicht am 06.06.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Volkswirtschaftslehre (ECON)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2190-9806
urn:nbn:de:swb:90-832796
KITopen-ID: 1000083279
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 19 S.
Serie Working paper series in economics ; 116
Schlagwörter stopping time, false alarm probability, average detection, delay, Bayes stopping time, CUSUM method, multiple hypothesis test-, ing
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page