A semiparametric approach to estimate reference curves for biophysical properties of the skin

Reference curves which take one covariable into account such as the 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). In this chapter, we describe a new methodology for the estimation of reference curves for data sets, based on nonparametric estimation of conditional quantiles. The derived method should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale. To avoid the curse of dimensionality when the covariate is multidimensional, a new semiparametric approach is proposed. Th…

Two-step Estimation in a Multivariate Semiparametric Sample Selection Model

International audience

Some extensions of multivariate sliced inverse regression

Multivariate sliced inverse regression (SIR) is a method for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we extend the existing approaches, based on the usual SIR I which only uses the inverse regression curve, to methods using properties of the inverse conditional variance. Contrary to the existing ones, these new methods are not blind for symmetric dependencies and rely on the SIR II or SIRα. We also propose their corresponding pooled slicing versions. We illustrate the usefulness of these approaches on simulation studies.

A Cluster-based Approach for Sliced Inverse Regression

International audience

Un estimateur de la médiane spatiale conditionnelle par transformation-retransformation.

Quantiles de régression : applications à la construction de courbes de référence

Asymptotics for pooled marginal slicing estimator based on SIRα approach

Pooled marginal slicing (PMS) is a semiparametric method, based on sliced inverse regression (SIR) approach, for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we consider the SIR"@a version (combining the SIR-I and SIR-II approaches) of the PMS estimator and we establish the asymptotic distribution of the estimated matrix of interest. Then the asymptotic normality of the eigenprojector on the estimated effective dimension reduction (e.d.r.) space is derived as well as the asymptotic distributions of each estimated e.d.r. direction and its corresponding eigenvalue.

Interaspecific chemical variability and highlighting of chemotypes of leaf essential oils from Ravensara aromatica Sonnerat, a tree endemic to Madagascar

Ravensara aromatica Sonnerat is a tree endemic to Madagascar. The essential oil extracted from the leaves is used in aromatherapy. Previous chemical studies have generated some confusion with regard to the chemical composition of this essential oil. In order to eliminate this uncertainty, we undertook a systematic evaluation of the chemical composition of essential oils from leaves of this species. The study focused on 28 individual samples formally identified as R. aromatica. The essential oils were obtained by hydrodistillation and analysed by GC and GC–MS. It was possible to distinguish four groups of trees through principal components analysis and agglomerative hierarchical clustering a…