Adaptive estimation with warped or incomplete data. Application to survival analysis
type: Dataset
description: This thesis presents various problems of adaptive functional estimation, using projection and kernel methods, and criterions inspired both by model selection and Lepski's methods. The common point of the studied statistical setting is to deal with transformed and/or incomplete data. The first part proposes a method of estimation with a "warping" device which permits to handle the estimation of functions such as additive and multiplicative regression, conditional density, hazard rate based on randomly right-censored data, and cumulative distribution function from current-status data. The aim is to estimate a function from a sample of random variable (X,Y). We use the warped data (ф(X),Y), to propose adaptive estimators, where ф is a one-to-one function that we also estimate (e.g. the cumulative distribution function of X). The interest is twofold. From the theoretical point of view, the estimators are optimal in the oracle sense. From the practical point of view, they can be easily computed, thanks to their simple explicit expression. The second part deals with a two-sample problem : we compare the distribution of two variables X and Xₒ by studying the relative density, defined as the density of Fₒ(X) (Fₒ is the c.d.f. of Xₒ). We build adaptive estimators, from a double data-sample, possibly censored. Non-asymptotic risk bounds are proved, and convergence rates are also derived.
identifier: NNT: 2013PA05S008
issued: 2026-05-09T17:06:31.484386
language: fr
modified: 2026-05-09T17:06:31.484390
contact point: Organization
  fn: CCSD
keyword: adaptative-estimation
keyword: bases-et-noyaux-deformes
keyword: censored-data
keyword: donnees-censurees
keyword: estimation-adaptative
keyword: infoeu-reposemanticsdoctoralthesis
keyword: lepskis-method
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: methode-de-lepski
keyword: model-selection
keyword: probeme-a-deux-echantilllons
keyword: regression
keyword: selection-de-modeles
keyword: theses
keyword: two-sample-problem
keyword: warped-bases-and-kernels
landing page: https://theses.hal.science/tel-00863141

Adaptive estimation with warped or incomplete data. Application to survival analysis
type: Distribution
format: HTML
issued: 2026-05-09T17:06:31.493765
modified: 2026-05-09T17:06:31.468498
access URL: https://theses.hal.science/tel-00863141

test_moissonnage_selune
type: Agent