Detection of Abnormal Behavior Via Nonparametric Estimation of the Support

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, we are given one new measurement and we wish to know whether or not it belongs to the support of. In the second problem, after observing the n independent random vectors with a common unknown distribution, we then observe n additional independent random vectors with a common unknown distribution. In this case we wish to know whether or not the support of is completely contained within the support of. Decision schemes are presented and then convergence properties are established.