[{"type":"report","title":"On robust stopping times for detecting changes in distribution","issued":{"date-parts":[["2018"]]},"DOI":"10.5445\/IR\/1000083279","author":[{"family":"Golubev","given":"Yuri"},{"family":"Safarian","given":"Mher"}],"publisher":"KIT","publisher-place":"Karlsruhe","ISSN":"2190-9806","collection-title":"Working paper series in economics","abstract":"Let X1, X2,...be independent random variables observed sequen-tially and such that X1,...,X \u03b8\u22121 have a common probability density p 0, while X \u03b8 ,X \u03b8 +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 \u03b8 \u2208 Z + is unknown and the goal is to construct a stopping time \u03c4 that detects the hange-point \u03b8 as soon as possible. The existing approaches to this problem rely essentially on some a priori information about \u03b8. For in-stance, in Bayes approaches, it is assumed that \u03b8 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 \u03b8, but have nearly Bayesian detection delays. More precisely, we propose stopping times solving approximately the following problem: \u2206 (\u03b8;\u03c4\u03b1) \u2192 min \u03c4\u03b1 subject to \u03b1 (\u03b8;\u03c4\u03b1) \u2264 \u03b1 for any \u03b8 \u2265 1, where \u03b1 (\u03b8; \u03c4 ) =\r\nP \u03b8 { \u03c4 < \u03b8} is the false alarm probability and \u2206(\u03b8;\u03c4) = E \u03b8 (\u03c4\u2212\u03b8) + is the average detection delay, and explain why such top-ping times are robust w.r.t. a priori information about \u03b8.","keyword":"stopping time, false alarm probability, average detection\r\ndelay, Bayes stopping time, CUSUM method, multiple hypothesis test-\r\ning","number-of-pages":19,"kit-publication-id":"1000083279"}]