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Journal Articles Statistics and Probability Letters Year : 2008

A note on extreme values and kernel estimators of sample boundaries

Abstract

In a previous paper, we studied a kernel estimate of the upper edge of a two-dimensional bounded set, based upon the extreme values of a Poisson point process. The initial paper "Geffroy J. (1964) Sur un problème d'estimation géométrique.Publications de l'Institut de Statistique de l'Université de Paris, XIII, 191-200" on the subject treats the frontier as the boundary of the support set for a density and the points as a random sample. We claimed in"Girard, S. and Jacob, P. (2004) Extreme values and kernel estimates of point processes boundaries.ESAIM: Probability and Statistics, 8, 150-168" that we are able to deduce the random sample case fr om the point process case. The present note gives some essential indications to this end, including a method which can be of general interest.
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Dates and versions

hal-00724899 , version 1 (23-08-2012)

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Stéphane Girard, Pierre Jacob. A note on extreme values and kernel estimators of sample boundaries. Statistics and Probability Letters, 2008, 78 (12), pp.1634-1638. ⟨10.1016/j.spl.2008.01.046⟩. ⟨hal-00724899⟩
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