Dimension reduction in regression
type: Dataset
description: In this thesis, we study the problem of dimension reduction through the following regression model Y=g(BX,e), where X is a p dimensional vector, Y belongs to R, the function g is unknown and the noise e is independent of X. We are interested in the estimation of the matrix B, with dimension d times p where d is smaller than p (whose knowledge provides good convergence rates for the estimation of g). This problem is processed according to two different approaches. The first one, called the inverse regression, needs the linearity condition on X. The second one, called semiparametric, do not require such an assumption but only that X has a smooth density. In the context of inverse regression, we focus on two families of methods respectively based on E[X f(Y)] and E[XX^T f(Y)]. For both families, we provide conditions on f that allow an exhaustive estimation of B, and also we compute the better function f by minimizing the asymptotic variance. In the semiparametric context, we give a method for the estimation of the gradient of the regression function. Under some classical semiparametric assumptions, we show the root n consistency of our estimator, the exhaustivity of the estimation and the convergence in the processes space. Within each point, an important question is raised : how to choose the dimension of B ? For this we propose a method that estimates of the rank of a matrix by bootstrap hypothesis testing.
identifier: NNT: 2013REN1S039
issued: 2026-05-09T10:48:37.891425
language: en
modified: 2026-05-09T10:48:37.891429
contact point: Organization
  fn: CCSD
keyword: average-derivative-estimator
keyword: estimation-du-gradient-de-la-regression
keyword: infoeu-reposemanticsdoctoralthesis
keyword: inverse-regression
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: modele-a-directions-revelatrices
keyword: multiple-index-model
keyword: reduction-de-la-dimension-en-regression
keyword: regression-inverse
keyword: sufficient-dimension-reduction
keyword: theses
landing page: https://theses.hal.science/tel-00871049

Dimension reduction in regression
type: Distribution
format: HTML
issued: 2026-05-09T10:48:37.911112
modified: 2026-05-09T10:48:37.870934
access URL: https://theses.hal.science/tel-00871049

test_moissonnage_selune
type: Agent