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Extreme values and kernel estimates of point processes boundaries

Stéphane GirardPierre Jacob — 2004

ESAIM: Probability and Statistics

We present a 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 a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

Extreme values and kernel estimates of point processes boundaries

Stéphane GirardPierre Jacob — 2010

ESAIM: Probability and Statistics

We present a 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 a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by some simulations.

Mean quadratic convergence of signed random measures

Pierre JacobPaulo Eduardo Oliveira — 1991

Commentationes Mathematicae Universitatis Carolinae

We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper.

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