Kernel estimation of density level sets

Authors:
Benoı^t Cadre
Affiliations:
UMR CNRS 5149, Equipe de Probabilités et Statistique, Université Montpellier II, CC 051, Place E. Bataillon, 34095 Montpellier Cedex 5, France
Venue:
Journal of Multivariate Analysis
Year:
2006

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Abstract

Let f be a multivariate density and f"n be a kernel estimate of f drawn from the n-sample X"1,...,X"n of i.i.d. random variables with density f. We compute the asymptotic rate of convergence towards 0 of the volume of the symmetric difference between the t-level set {f=t} and its plug-in estimator {f"n=t}. As a corollary, we obtain the exact rate of convergence of a plug-in-type estimate of the density level set corresponding to a fixed probability for the law induced by f.