On robust stopping times for detecting changes in distribution

Yuri Golubev and Mher M. Safarian

No 116, Working Paper Series in Economics from Karlsruhe Institute of Technology (KIT), Department of Economics and Management

Abstract: Let X1,X2,… be independent random variables observed sequentially and such that X1,…,Xθ−1 have a common probability density p0, while Xθ,Xθ+1,… are all distributed according to p1≠p0. It is assumed that p0 and p1 are known, but the time change θ∈Z+ is unknown and the goal is to construct a stopping time τ that detects the change-point θ as soon as possible. The existing approaches to this problem rely essentially on some a priori information about θ. For instance, 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 average run length. The main goal in this paper is to construct stopping times which do not make use of a priori information about θ, but have nearly Bayesian detection delays. More precisely, we propose stopping times solving approximately the following problem: Δ(θ;τα)→minτα subject to α(θ;τα)≤α for any θ≥1, where α(θ;τ)=Pθ{τ

Keywords: stopping time; false alarm probability; average detection delay; Bayes stopping time; CUSUM method; multiple hypothesis testing (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:kitwps:116

DOI: 10.5445/IR/1000083279

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