Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download

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

Files

DiBernadino_Laloe.pdf
Files produced by the author(s)

Identifiers

  • 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⟩

Share

Metrics

Record views

286

Files downloads

164