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Uncertain change-point problem for stochastic sequence

机译:随机序列的不确定变点问题

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摘要

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.
机译:考虑了一系列独立随机变量的变化点问题。更改点之前和之后的随机变量分布是未知的,但先验已知可能分布的有限集合。因此,问题是在没有任何有关其方向的信息的情况下检测更改(“不确定的更改点问题”)。针对变化点检测方法的质量估计,提出了一种新的向量准则。对于此标准,获得了非渐近下界。提出了一种快速检测不确定变化点的方法,该方法渐近地实现了这些下界。

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