Nonparametric estimation for additive concurrent regression models - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Nonparametric estimation for additive concurrent regression models

Fabienne Comte
Céline Duval
  • Fonction : Auteur
  • PersonId : 1129868

Résumé

We consider an additive functional regression model where the responses are $N$ {\it i.i.d.} one-dimensional processes $(Y_i(t), i=1, \ldots, N)$ and the $K$ explanatory random processes $X_{i,j}(t)$ for $j=1, \dots, K$ are observed for $t\in [0,\tau]$, $\tau$ being fixed. The coefficients in the model are $K$ unknown functions $t\mapsto b_j(t)$ for $j=1, \dots, K$ and we build nonparametric least squares estimators under several general settings of explanatory processes, for example, continuous or inhomogeneous counting processes. We bound a mean-square type risk of the estimators from which rates of convergence are deduced. Optimality of the rates is established. An adaptive procedure is then taylored and proved to lead to relevant anisotropic model selection, simultaneously for all functions. Numerical illustrations and a real data example show the practical interest of the theoretical strategy.
Fichier principal
Vignette du fichier
ConcurrentRegression-4-1.pdf (2.17 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04600808 , version 1 (04-06-2024)

Identifiants

  • HAL Id : hal-04600808 , version 1

Citer

Elodie Brunel, Fabienne Comte, Céline Duval. Nonparametric estimation for additive concurrent regression models. 2024. ⟨hal-04600808⟩
21 Consultations
13 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More