Polychotomous regression : application to landcover prediction

An important field of investigation in Geography is the modelization of the evolution of land cover in view of analyzing the dynamics of this evolution and then to build predictive maps. This is possible with the apparatus of measure : sattelite image... In this paper, we propose to use a polychotomous regression model to modelize and to predict land cover of a given area : we shox how to adapt this model in order to take into account the spatial correlation and the temporal evolution of the vegetation indexes. This study concerns an area in the Pyrenees mountains

Smoothing splines estimators for functional linear regression

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a slight modification of the usual penalty. Theoretical analysis concentrates on the error in an out-of-sample prediction of the response for a new random function $X_{n+1}$. It is shown that rates of convergence of the prediction error depend on the smoothness of the slope function and on the structure of the predictors. We then prove that these rates are optimal in the sense that they are minimax over large classes of possible slope functions and distributions of the predictive curves. For the case of models with errors-in-variables the smoothing spline estimator is modified by using a denoising correction of the covariance matrix of discretized curves. The methodology is then applied to a real case study where the aim is to predict the maximum of the concentration of ozone by using the curve of this concentration measured the preceding day.Comment: Published in at http://dx.doi.org/10.1214/07-AOS563 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimation spline de quantiles conditionnels pour variables explicatives fonctionnelles

International audienceCette Note a pour objet un modèle de régression linéaire sur quantiles lorsque la variable explicative est à valeurs dans un espace fonctionnel alors que la variable réponse est réelle. Nous proposons un estimateur spline du coefficient fonctionnel basé sur la minimisation d'un critère de type L1 pénalisé (la pénalisation est primordiale pour avoir l'existence et la convergence de l'estimateur), puis nous étudions le comportement asymptotique de cet estimateur

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.Comment: 14 pages; Classifications: Information Theory; Probability Theory & Applications; Statistical Computing; Statistical Theory & Method

CLT in Functional Linear Regression Models

International audienceWe propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator. Rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made

Clinical, Biological and Genetic Analysis of Prepubertal Isolated Ovarian Cyst in 11 Girls

BACKGROUND: The cause of isolated gonadotropin-independent precocious puberty (PP) with an ovarian cyst is unknown in the majority of cases. Here, we describe 11 new cases of peripheral PP and, based on phenotypes observed in mouse models, we tested the hypothesis that mutations in the GNAS1, NR5A1, LHCGR, FSHR, NR5A1, StAR, DMRT4 and NOBOX may be associated with this phenotype. METHODOLOGY/PRINCIPAL FINDINGS: 11 girls with gonadotropin-independent PP were included in this study. Three girls were seen for a history of prenatal ovarian cyst, 6 girls for breast development, and 2 girls for vaginal bleeding. With one exception, all girls were seen before 8 years of age. In 8 cases, an ovarian cyst was detected, and in one case, suspected. One other case has polycystic ovaries, and the remaining case was referred for vaginal bleeding. Four patients had a familial history of ovarian anomalies and/or infertility. Mutations in the coding sequences of the candidate genes GNAS1, NR5A1, LHCGR, FSHR, NR5A1, StAR, DMRT4 and NOBOX were not observed. CONCLUSIONS/SIGNIFICANCE: Ovarian PP shows markedly different clinical features from central PP. Our data suggest that mutations in the GNAS1, NR5A1, LHCGR, FSHR StAR, DMRT4 and NOBOX genes are not responsible for ovarian PP. Further research, including the identification of familial cases, is needed to understand the etiology of ovarian PP