Detection of Abnormal Behavior Via Nonparametric Estimation of the Support

Abstract

In this paper two problems are considered, both involving the nonparametric estimation of the support of a random vector from a sequence of independent identically distributed observations. In the first problem, after observing n independent random vectors with a common unknown distribution $\mu $, we are given one new measurement and we wish to know whether or not it belongs to the support of $\mu $. In the second problem, after observing the n independent random vectors with a common unknown distribution $\mu $, we then observe n additional independent random vectors with a common unknown distribution $\nu $. In this case we wish to know whether or not the support of $\nu $ is completely contained within the support of $\mu $. Decision schemes are presented and then convergence properties are established.