Section: New Results

New functional regression model when data are auto-correlated

Participant : Sophie Dabo.

We develop a new functional regression model when data are auto-correlated, in collaboration with Serge Guillas (University of College London) and Camille Ternynck (University of Lille 2). This work will appear in Journal of Multivariate Analysis. ( Dabo-Niang, S, Guillas, S et Ternynck, C. (2016). More efficient kernel functional spatial regression estimation with autocorrelated errors. Journal of Multivariate Analysis). In this work we introduce a new procedure for the estimation in the nonlinear functional regression model where the explanatory variable takes values in an abstract function space and the residual process is autocorrelated. The procedure consists in a pre-whitening transformation of the dependent variable based on the estimated autocorrelation. We establish both consistency and asymptotic normality of the regression function estimate. For kernel methods encountered in the literature, the correlation structure is commonly ignored (the so-called “working independence estimator”); we show here that there is a strong benefit in taking into account the autocorrelation in the error process. We also find that the improvement in efficiency can be large in our functional setting, up to 25% in the presence of high autocorrelation levels. Concerning spatial data, we develop a new spatial prediction method that takes into account the spatial dependence. This work will appear in Journal of Nonparametric Statistics (Dabo-Niang, Ternynck, C., Yao, A.-F. (2016). Nonparametric prediction in the multivariate spatial context. Journal of Nonparametric Statistics)