Nonparametric estimation for additive ...
Document type :
Pré-publication ou Document de travail
Permalink :
Title :
Nonparametric estimation for additive concurrent regression models
Author(s) :
Brunel, Elodie [Auteur]
Institut Montpelliérain Alexander Grothendieck [IMAG]
Comte, Fabienne [Auteur]
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]
Duval, Céline [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut Montpelliérain Alexander Grothendieck [IMAG]
Comte, Fabienne [Auteur]
Mathématiques Appliquées Paris 5 [MAP5 - UMR 8145]
Duval, Céline [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
English keyword(s) :
Adaptive estimation
Continuous observation
Functional data
Least squares estimator
Nonparametric regression function estimation
Projection method
Continuous observation
Functional data
Least squares estimator
Nonparametric regression function estimation
Projection method
HAL domain(s) :
Statistiques [stat]
Mathématiques [math]
Mathématiques [math]
English abstract : [en]
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, ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Collections :
Source :
Submission date :
2025-01-24T12:54:28Z
Files
- document
- Open access
- Access the document
- ConcurrentRegression-4-1.pdf
- Open access
- Access the document