Stéphane Girard

Sliced Inverse Regression In Reference Curves Estimation

In order to obtain reference curves for data sets when the covariate is multidimensional, a new procedure is proposed. This procedure is based on dimension-reduction and non-parametric estimation of conditional quantiles. This semiparametric approach combines sliced inverse regression (SIR) and a kernel estimation of conditional quantiles. The asymptotic convergence of the derived estimator is shown. By a simulation study, this procedure is compared to the classical kernel non-parametric one for different dimensions of the covariate. The semiparametric estimator shows the best performance. The usefulness of this estimation procedure is illustrated on a real data set collected in order to establish reference curves for biophysical properties of the skin of healthy French women.

Extreme Values and Haar Series Estimates of Point Process Boundaries

We present a new method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on Haar series and extreme values of the point process. We give conditions for various kind of convergence and we obtain remarkably different possible limit distributions. We propose a method of reducing the negative bias, illustrated by a simulation. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..

Projection estimates of point processes boundaries

Abstract We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on projections on C1 bases and on extreme points of the point process. We give conditions on the Dirichlets kernel associated to the C1 bases for various kinds of convergence and asymptotic normality. We propose a method for reducing the negative bias and illustrate it by a simulation.

A note on the asymptotic normality of the ET method for extreme quantile estimation

In this note, we establish the asymptotic distribution of the exponential tail estimator of extreme quantiles. We give sufficient conditions for the asymptotic normality and provide some illustrating examples.

Consistance de la méthode ET et variations régulières

Abstract We define the k -th order approximation of an extreme quantile q α n , α n n , and study its consistency as α n → 0 and n → ∞ for classes of distributions in Gumbels maximum domain of attraction. We show that the consistency of the k -th order approximation imposes conditions on α n in most cases, but does not depend on k . As a particular case, we obtain that, when the ET approximation (which is also the first-order approximation) is consistent, then the quantile q α n can also be consistently approximated by the maximal observation. When an approximation is consistent, we give the rate of convergence to zero of the relative approximation error.