Kernel Estimation of Density Level Sets

2005/01/14 by Benoı̂t Cadre, Cadre, Benoit · 1 citation
Computer Science · Mathematics · #62H12 #62H30 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0501221

openalex publication_date 2005/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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