Uncertain Change-Point Problem for Stochastic Sequence
Boris Semenovich Darkhovsky · Theory of Probability and Its Applications · 2012
The change-point problem for a sequence of independent random variables is considered. Distributions of random variables before and after a change-point are unknown, but a finite collection of possible distributions is known a priori. Therefore, the problem is to detect the change without any information about its direction (an “uncertain change-point problem”). A new vector criterion to be minimized is proposed for change-point detection method quality estimation. For this criterion, nonasymptotic lower bounds are obtained. A method of quickest detection of the uncertain change-point is proposed for which these lower bounds are asymptotically attained.