Set estimation and nonparametric detection

The authors consider the estimation of a set S subset of R(d) from a random sample of n points. They examine the properties of a detection method, proposed by Devroye & Wise (1980), which relies on the use of a "naive" estimator of S defined as a union of balls centered at the sample points with common radius epsilon (n). They obtain the convergence rate for the probability of false alarm and show that the smoothing parameter epsilon (n) can be used to incorporate some prior information on the shape of S. They suggest two general methods for selecting epsilon (n) and illustrate them with a simulation study and a real data example.