Kernel Estimation of Density Level Sets

Benoit Cadre

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Kernel Estimation of Density Level Sets

Benoit Cadre

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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 $\{f\geq t\}$ and its plug-in estimator $\{f\_n\geq t\}$. 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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Benoit Cadre. 2005-01-14. Kernel Estimation of Density Level Sets. https://arxiv.org/abs/math/0501221

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