Robust quantile estimation and prediction for spatial processes

In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional quantile estimator in the case of random fields. We also define a nonparametric spatial predictor and illustrate the methodology used with some simulations.Comment: 13 page

Combining parametric and nonparametric approaches for more efficient time series prediction

We introduce a two-step procedure for more efficient nonparametric prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as explanatory variables. Compared to standard nonparametric regression methods, the number of explanatory variables can be reduced because our approach exploits the linear dependence of the process. We establish consistency and asymptotic normality results for our estimator. A Monte Carlo study and an empirical application on stock market indices suggest that significant gains can be achieved with our approach.ARMA representation; noisy data; Nonparametric regression; optimal prediction

Régression et prédiction non-paramétrique spatiale

International audienceNous nous intéressons à l'estimation de la fonction de régression r(x)=E\left(Y_{\mathbfu}|X_{\mathbfu}=x\right) à partir d'observations d'un processus \left\{ Z_{\mathbfi}=\left(X_{\mathbfi},\ Y_{\mathbfi}\right),\,\mathbfi\in\mathbbZ^N\right\}. On suppose que les variables Z_{\mathbfi}$sont de même distribution que$Z=(X,Y)$, où$Y$est une variable réelle, intégrable et$X$un vecteur aléatoire à valeurs dans un espace séparable$\mathcalE$muni (éventuellement de dimension infinie). Dans ce travail, la convergence nos estimateurs est étudiée sous conditions de mélange à partir d'observations dans une région rectangulaire de$\mathbbZ^N$. Nous illustrerons nos résultats par des simulations. L'application de nos méthodes à la prédiction spatiale sera également abordée

KERNEL SPATIAL DENSITY ESTIMATION IN INFINITE DIMENSION SPACE

In this paper, we propose a nonparametric estimation of the spatial density of a functional stationary random field. This later is with values in some infinite dimensional space and admitted a density with respect to some reference measure. The weak and strong consistencies of the estimator are shown and rates of convergence are given. Special attention is paid to the links between the probabilities of small balls in the concerned infinite dimensional space and the rates of convergence. The practical use and the behavior of the estimator are illustrated through some simulations and a real data application

k-nearest neighbors prediction and classification for spatial data

We propose a nonparametric predictor and a supervised classification based on the regression function estimate of a spatial real variable using k-nearest neighbors method (k-NN). Under some assumptions, we establish almost complete or sure convergence of the proposed estimates which incorporate a spatial proximity between observations. Numerical results on simulated and real fish data illustrate the behavior of the given predictor and classification method

Spatial mode estimation for functional random fields with application to bioturbation problem

This work provides a useful tool to study the effects of bioturbation on the distribution of oxygen within sediments. We propose here heterogeneity measurements based on functional spatial mode. To obtain the mode, one usually needs to estimate the spatial probability density. The approach considered here consists in looking each observation as a curve that represents the history of the oxygen concentration at a fixed pixel