Asymptotic statistical properties of communication-efficient quickest detection schemes in sensor networks

Abstract

The quickest change detection problem is studied in a general context of monitoring a large number K of data streams in sensor networks when the “trigger event” may affect different sensors differently. In particular, the occurring event might affect some unknown, but not necessarily all, sensors and also could have an immediate or delayed impact on those affected sensors. Motivated by censoring sensor networks, we develop scalable communication-efficient schemes based on the sum of those local cumulative sum (CUSUM) statistics that are “large” under either hard, soft, or order thresholding rules. Moreover, we provide the detection delay analysis of these communication-efficient schemes in the context of monitoring K independent data streams and establish their asymptotic statistical properties under two regimes: one is the classical asymptotic regime when the dimension K is fixed, and the other is the modern asymptotic regime when the dimension K goes to ∞. Our theoretical results illustrate the deep connections between communication efficiency and statistical efficiency.

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