A note on extreme values and kernel estimators of sample boundaries

摘要

In a previous paper [Girard, S., Jacob, P., 2004. Extreme values and kernel estimates of point processes boundaries. ESAIM: Probability and Statistics 8, 150-168], 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 probleme d'estimation geometrique. Publications de l'Institut de Statistique de l'Universite 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 our 2004 paper (cited above) that we are able to deduce the random sample case from the point process case. The present note gives some essential indications to this end, including a method which can be of general interest.