On the semiparametric robust estimation in functional statistic
type: Dataset
description: In this thesis, we propose to study some functional parameters when the data are generated from a model of regression to a single index. We study two functional parameters. Firstly, we suppose that the explanatory variable take its values in Hilbert space (infinite dimensional space) and we consider the estimate of the conditional density by the kernel method. We establish some asymptotic properties of this estimator in both independent and dependent cases. For the case where the observations are independent identically distributed (i.i.d.), we obtain the pointwise and uniform almost complete convergence with rateof the estimator. As an application we discuss the impact of this result in fuctional nonparametric prevision for the estimation of the conditional mode. In the dependent case we modelize the later via the quasi-associated correlation. Note that all these asymptotic properties are obtained under standard conditions and they highlight the phenomenon of concentration properties on small balls probability measure of the functional variable. Secondly we suppose that the explanatory variable takes values in the _nite dimensional space and we interest in a rather general prevision model whichis the robust regression. From the quasi-associated data, we build a kernel estimator for this functional parameter. As an asymptotic result we establish the uniform almost complete convergence rate of the estimator. We point out by the fact that these two models studied in this thesis could be used for the estimation of the single index of the model when the latter is unknown, by using the method of M-estimation or the pseudo-maximum likelihood method which is a particular case of the first method.
landing page: https://theses.hal.science/tel-00871026
identifier: NNT: 2012DUNK0325
keyword: estimation-non-parametrique
keyword: estimation-semi-parametrique
keyword: functional-data
keyword: indice-simple
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: nonparametric-estimation
keyword: quasi-associated-dependent-variables
keyword: regression-robuste
keyword: semiparametric-estimation
keyword: single-index
keyword: statisque-fonctionnelle
keyword: theses
issued: 2026-05-09T10:49:12.235544
modified: 2026-05-09T10:49:12.235550
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

On the semiparametric robust estimation in functional statistic
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00871026
issued: 2026-05-09T10:49:12.252605
modified: 2026-05-09T10:49:12.217452