Bootstrapping convex hulls

If the distribution of observations satisfies a multivariate regular variation condition then the asymptotic distribution of convex hulls can be modeled by using point processes. The limiting distributions cannot be simplified and are extremely difficult to use. We show the bootstrap is asymptotically valid if the resampling sample size is m = o(n), where n is the original sample size. We use this to also provide an asymptotically valid bootstrap for the area and perimeter of the convex hulls. Also, under a circularly symmetric distribution an alternative and consistent Monte Carlo method is studied. (C) 1999 Elsevier Science B.V. All rights reserved.