F. Ferraty (Institut Mathématique de Toulouse) : Parsimonious and Nonparametric Regression in high-dimensional settings

Date(s) : 20/05/2014   iCal
10 h 00 min - 11 h 00 min

Parsimonious and Nonparametric Regression in high-dimensional settings\n\nBy Frédéric Ferraty\, Institut Mathématique de Toulouse\n\nThe high dimensional setting is a modern and dynamic research area in Statistics. It covers numerous situations where the number of explanatory variables is much larger than the sample size. Last fifteen years have been devoted to develop new methodologies able to manage high dimensional data including the so-called functional data (which can be viewed as a special case of high dimensional data with a high correlated structure). In this talk we especially focus on the situation when a scalar response is regressed on a large number of covariates. Parsimonious models have been intensively developed in this high-dimensional framework but essentially under linear assumption. However\, it is well known in the nonparametrician community that taking into account nonlinearities may improve significantly the predictive power of the statistical methods and also may reveal relevant informations allowing to better understand the observed phenomenon. In the first part of this talk we propose a new algorithm for selecting nonlinearly (nonparametrically) few covariates involved in a nonparametric regression model. This nonparametric variable selection method allows to reduce significantly the number of retained covariates while improving the predictive power in comparison with the standard linear alternative called lasso. A genomic dataset will illustrate the finite-sample behaviour. In the second part\, this nonparametric variable selection is applied to datasets containing near-infrared spectra (functional data) considered as multivariate data. One dataset deals with a petroleum prediction problem whereas a second one concerns a standard food industry dataset. This nonparametric parsimonious “functional” data analysis is compared with the nonparametric functional regression (full functional method) which emphasizes some advantages of the proposed selective method from both interpretability and predictive viewpoints.

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