# Estimating level sets of a distribution function using a plug-in method: a multidimensional extension

Abstract : This paper deals with the problem of estimating the level sets $L(c)= \{F(x) \geq c \}$, with $c \in (0,1)$, of an unknown distribution function $F$ on \mathbb{R}^d_+$. A plug-in approach is followed. That is, given a consistent estimator$F_n$of$F$, we estimate$L(c)$by$L_n(c)= \{F_n(x) \geq c \}\$. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. These results can be considered as generalizations of results previously obtained, in a bivariate framework, in Di Bernardino et al. (2011). Finally we investigate the effects of scaling data on our consistency results.
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Cited literature [12 references]

https://hal.archives-ouvertes.fr/hal-00668317
Contributor : Thomas Laloe <>
Submitted on : Thursday, February 9, 2012 - 3:45:41 PM
Last modification on : Monday, October 12, 2020 - 10:27:31 AM
Long-term archiving on: : Thursday, May 10, 2012 - 2:46:19 AM

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• HAL Id : hal-00668317, version 1
• ARXIV : 1202.2035

### Citation

Elena Di Bernadino, Thomas Laloë. Estimating level sets of a distribution function using a plug-in method: a multidimensional extension. 2012. ⟨hal-00668317⟩

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