Extreme values and kernel estimates of point processes boundaries

Stéphane Girard; Pierre Jacob

ESAIM: Probability and Statistics (2010)

  • Volume: 8, page 150-168
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Girard, Stéphane, and Jacob, Pierre. "Extreme values and kernel estimates of point processes boundaries." ESAIM: Probability and Statistics 8 (2010): 150-168. <http://eudml.org/doc/104316>.

@article{Girard2010,
abstract = { 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. },
author = {Girard, Stéphane, Jacob, Pierre},
journal = {ESAIM: Probability and Statistics},
keywords = {Kernel estimates; extreme values; Poisson process; shape estimation.; shape estimation},
language = {eng},
month = {3},
pages = {150-168},
publisher = {EDP Sciences},
title = {Extreme values and kernel estimates of point processes boundaries},
url = {http://eudml.org/doc/104316},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Girard, Stéphane
AU - Jacob, Pierre
TI - Extreme values and kernel estimates of point processes boundaries
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 150
EP - 168
AB - 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.
LA - eng
KW - Kernel estimates; extreme values; Poisson process; shape estimation.; shape estimation
UR - http://eudml.org/doc/104316
ER -

References

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