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依赖数据流的联合序贯检测与定位AI 解读

The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the…

变化的加速与检测AI 解读

A novel sequential change detection problem is proposed, in which the goal is to not only detect but also accelerate the change. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected in real time. The assigned treatments determine the pre-change and post-change distributions of the responses and also influence when the change happens. The goal is to find a treatment assignment rule and a stopping rule that minimize the…

广义错误控制下序贯多重检验的渐近最优性理论AI 解读

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_{1}$ false positives and at least $k_{2}$ false negatives are simultaneously controlled. For each formulation, the optimal expected sample size is characterized, to a first-order asymptotic approximation as the error probabilities go to 0, and a…

通信约束下渐近最优的参数估计AI 解读

A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear with respect to a common parameter. A novel estimating scheme is suggested, according to which each sensor transmits only one-bit messages at stopping times of its local filtration. The proposed estimator is shown to be consistent and, for a…