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Extreme Values and Haar Series Estimates of Point Process Boundaries
Author(s) -
Girard Stéphane,
Jacob Pierre
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00336
Subject(s) - mathematics , extreme value theory , estimator , series (stratigraphy) , point process , haar , extreme point , convergence (economics) , bounded function , limit (mathematics) , point (geometry) , mathematical analysis , statistics , combinatorics , geometry , artificial intelligence , computer science , paleontology , wavelet , economics , biology , economic growth
. 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.