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UID:8361@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140520T100000
DTEND;TZID=Europe/Paris:20140520T110000
DTSTAMP:20241120T210348Z
URL:https://www.i2m.univ-amu.fr/evenements/f-ferraty-institut-mathematique
 -de-toulouse-parsimonious-and-nonparametric-regression-in-high-dimensional
 -settings/
SUMMARY: (...): F. Ferraty (Institut Mathématique de Toulouse) : Parsimoni
 ous and Nonparametric Regression in high-dimensional settings
DESCRIPTION:: 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 S
 tatistics. It covers numerous situations where the number of explanatory v
 ariables 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 regres
 sed on a large number of covariates. Parsimonious models have been intensi
 vely developed in this high-dimensional framework but essentially under li
 near assumption. However\\\, it is well known in the nonparametrician comm
 unity that taking into account nonlinearities may improve significantly th
 e predictive power of the statistical methods and also may reveal relevant
  informations allowing to better understand the observed phenomenon. In th
 e first part of this talk we propose a new algorithm for selecting nonline
 arly (nonparametrically) few covariates involved in a nonparametric regres
 sion model. This nonparametric variable selection method allows to reduce 
 significantly the number of retained covariates while improving the predic
 tive power in comparison with the standard linear alternative called lasso
 . A genomic dataset will illustrate the finite-sample behaviour. In the se
 cond part\\\, this nonparametric variable selection is applied to datasets
  containing near-infrared spectra (functional data) considered as multivar
 iate 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 nonparametri
 c functional regression (full functional method) which emphasizes some adv
 antages of the proposed selective method from both interpretability and pr
 edictive viewpoints.
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