Detection of Abnormal Behavior Via Nonparametric Estimation of the Support

Source 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.