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

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

2012-02-09

arxiv.org/abs/1202.2035v1

Mathematics

Statistics Theory

Scientific paper

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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