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A note on extreme values and kernel estimators of sample boundaries

Stephane Girard 1 Pierre Jacob 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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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Stephane Girard, Pierre Jacob. A note on extreme values and kernel estimators of sample boundaries. Statistics and Probability Letters, Elsevier, 2008, 78 (12), pp.1634-1638. ⟨10.1016/j.spl.2008.01.046,⟩. ⟨hal-00724899⟩

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