Louis Ferré

Determining the Dimension in Sliced Inverse Regression and Related Methods

Abstract Sliced inverse regression (SIR) and principal Hessian directions aim to reduce the dimensionality of regression problems. An important step in the method is the determination of a suitable dimension. Although statistical tests based on the nullity eigenvalues are usually suggested, this article focuses on the quality of the estimation of the effective dimension reduction (EDR) spaces. Essentially, the goal is to retain only sufficiently stable subspaces. The goodness of the estimation is measured by the squared trace correlation between the subspaces of the EDR space and their estimates. Asymptotic expansions are derived and estimates deduced. Simulations give an insight on the behavior of the criterion and indicate how it can be used in practice.

Various Approaches for Predicting Land Cover in Mountain Areas

Using former maps, geographers intend to study the evolution of the land cover in order to have a prospective approach on the future landscape; predictions of the future land cover, by the use of older maps and environmental variables, are usually done through the GIS (Geographic Information System). We propose here to confront this classical geographical approach with statistical approaches: a linear parametric model (polychotomous regression modeling) and a nonparametric one (multilayer perceptron). These methodologies have been tested on two real areas on which the land cover is known at various dates; this allows us to emphasize the benefit of these two statistical approaches compared to GIS and to discuss the way GIS could be improved by the use of statistical models.

Prospective modelling of environmental dynamics: A methodological comparison applied to mountain land cover changes

During the last 10 years, scientists have made significant advances in modelling environmental dynamics. A wide range of new methodological approaches in geomatics –such as neural networks, multi-agent systems or fuzzy logics– have been developed. Despite this progress, the modelling softwares available have to be considered as experimental tools rather than improved procedures that are able to work for environmental management or decision support. In particular, the authors think that a large number of publications suffer from discrepancies, when trying to validate their model’s results.