Adaptive estimation of marginal random-effects densities in linear mixed-effects models

Abstract : In this paper we consider the problem of adaptive estimation of random-effects densities in linear mixed-effects model. The linear mixed-effects model is defined as $Y_{k,j} = \alpha_k + \beta_k t_j + \varepsilon_{k,j}$ where $Y_{k,j}$ is the observed value for individual $k$ at time $t_j$ for $k=1,\ldots, N$ and $j=1,\ldots , J$. Random variables $(\alpha_k, \beta_k)$ are known as random effects and stand for the individual random variables of entity $k$. We denote their densities $f_\alpha$ and $f_\beta$ and assume that they are independent of the measurement errors $(\varepsilon_{k,j})$. We introduce kernel estimators and present upper risk bounds. We also give rates of convergence. The focus of this work lies on the optimal data driven choice of the smoothing parameter using a penalization strategy in the particular case of fixed interval between times $t_j$.
Type de document :
Article dans une revue
Mathematical Methods of Statistics, Allerton Press, Springer (link), 2015, 24 (2), pp.81-102. <10.3103/S1066530715020015>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00958905
Contributeur : Gwennaëlle Mabon <>
Soumis le : vendredi 17 avril 2015 - 12:02:24
Dernière modification le : samedi 18 février 2017 - 01:10:44

Fichier

MABON_random_effects_V4.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Gwennaëlle Mabon. Adaptive estimation of marginal random-effects densities in linear mixed-effects models. Mathematical Methods of Statistics, Allerton Press, Springer (link), 2015, 24 (2), pp.81-102. <10.3103/S1066530715020015>. <hal-00958905v4>

Partager

Métriques

Consultations de
la notice

126

Téléchargements du document

199