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