Extreme Values and Haar Series Estimates of Point Process Boundaries

We present a new method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on Haar series and extreme values of the point process. We give conditions for various kind of convergence and we obtain remarkably different possible limit distributions. We propose a method of reducing the negative bias, illustrated by a simulation. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..