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

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

Classification of multivariate functional data on different domains with Partial Least Squares approaches

Classification (supervised-learning) of multivariate functional data is considered when the elements of the random functional vector of interest are defined on different domains. In this setting, PLS classification and tree PLS-based methods for multivariate functional data are presented. From a computational point of view, we show that the PLS components of the regression with multivariate functional data can be obtained using only the PLS methodology with univariate functional data. This offers an alternative way to present the PLS algorithm for multivariate functional data.Comment: enhance readability, new simulation setting, correction of minor mathematical notations errors, rewrite the conclusio

Streamflow forecasting using functional regression

Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To this end, this paper introduces the functional linear models and adapts it to hydrological forecasting. More precisely, functional linear models are regression models based on curves instead of single values. They allow to consider the whole process instead of a limited number of time points or features. We apply these models to analyse the flow volume and the whole streamflow curve during a given period by using precipitations curves. The functional model is shown to lead to encouraging results. The potential of functional linear models to detect special features that would have been hard to see otherwise is pointed out. The functional model is also compared to the artificial neural network approach and the advantages and disadvantages of both models are discussed. Finally, future research directions involving the functional model in hydrology are presented