Sophie Dabo-Niang

Nonparametric Quantile Regression Estimation for Functional Dependent Data

Let (X i , Y i ) i=1,…, n be a sequence of strongly mixing random variables valued in ℱ × ℝ, where ℱ is a semi-metric space. We consider the problem of estimating the quantile regression function of Y i given X i . The principal aim of the article is to prove the consistency in L p norm of the proposed kernel estimate. The usefulness of the estimation is illustrated by a real data application where we are interested in forecasting hourly ozone concentration in the south-east of French.

Consistency of a nonparametric conditional quantile estimator for random fields

Given a stationary multidimensional spatial process (Zi = (Xi, Yi) ∈ ℝd × ℝ, i ∈ ℤN), we investigate a kernel estimate of the spatial conditional quantile function of the response variable Yi given the explicative variable Xi. Almost complete convergence and consistency in L2r norm (r ∈ ℕ*) of the kernel estimate are obtained when the sample considered is an α-mixing sequence.

Density estimation by orthogonal series in an infinite dimensional space: Application to processes of diffusion type I

In this paper, we will be concerned with the estimation of the probability density of a diffusion process with respect to the Wiener measure. Since a diffusion process can be viewed as a random variable taking its values in an infinite dimensional space, this problem can be viewed as a special case of estimating the probability density of a random variable with values in an infinite dimensional space. However, obtaining the absolute continuity of probability measures in infinite dimension is difficult. A density estimator based on a Fourier–Hermite orthogonal series is investigated, which is a generalization of the classical density estimator of a real valued random variable. We establish that our estimator converges in integrated and simple mean square, under suitable conditions. Rates of convergence are also given.

Nonparametric prediction of spatial multivariate data

This paper investigates a nonparametric spatial predictor of a stationary multidimensional spatial process observed over a rectangular domain. The proposed predictor depends on two kernels in order to control both the distance between observations and that between spatial locations. The uniform almost complete consistency and the asymptotic normality of the kernel predictor are obtained when the sample considered is an alpha-mixing sequence. Numerical studies were carried out in order to illustrate the behaviour of our methodology both for simulated data and for an environmental data set.