Stéphane Girard

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Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that highdimensional data usually live in different low-dimensional subspaces hidden in the original space. This paper presents a family of Gaussian mixture models designed for highdimensional data(More)
In the supervised classification framework, human supervision is required for labeling a set of learning data which are then used for building the classifier. However, in many applications, human supervision is either imprecise, difficult or expensive. In this paper, the problem of learning a supervised multiclass classifier from data with uncertain labels(More)
Reference curves which take time into account, such as those for age, are often required in medicine, but simple systematic and efficient statistical methods for constructing them are lacking. Classical methods are based on parametric fitting (polynomial curves). Semi-parametric methods are also widely used especially in Europe. Here, we propose a new(More)
In order to obtain reference curves for data sets when the covariate is multidimensional, we propose in this paper a new procedure based on dimension-reduction and nonparametric estimation of conditional quantiles. This semiparametric approach combines sliced inverse regression (SIR) and a kernel estimation of conditional quantiles. The asymptotic(More)
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an exponential regression model that was introduced in Diebolt et al. (2008). The asymptotic normality of the extreme(More)
A semiparametric regression model of a q-dimensional multivariate response y on a p-dimensional covariate x is considered. A new approach is proposed based on sliced inverse regression (SIR) for estimating the effective dimension reduction (EDR) space without requiring a prespecified parametric model. The convergence at rate √ n of the estimated EDR space(More)
This paper is concerned with the estimation of a local measure of intrinsic dimensionality (ID) recently proposed by Houle. The local model can be regarded as an extension of Karger and Ruhl's expansion dimension to a statistical setting in which the distribution of distances to a query point is modeled in terms of a continuous random variable. This form of(More)
We propose new estimates for the frontier of a set of points. They are de ned as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinations of kernel functions applied to the points of the sample. The coe cients of the linear combination are then computed by solving a linear(More)