Set estimation and nonparametric detection

The authors consider the estimation of a set S ? 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 ?_n. They obtain the convergence rate for the probability of false alarm and show that the smoothing parameter ?_n can be used to incorporate some prior information on the shape of S. They suggest two general methods for selecting ?_n and illustrate them with a simulation study and a real data example.