# 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 $t_j$.
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Article dans une revue
Mathematical Methods of Statistics, Allerton Press, Springer (link), 2015, 24 (2), pp.81-102. 〈10.3103/S1066530715020015〉
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https://hal.archives-ouvertes.fr/hal-00958905
Contributeur : Gwennaëlle Mabon <>
Soumis le : vendredi 17 avril 2015 - 12:02:24
Dernière modification le : mardi 10 octobre 2017 - 11:22:04
Document(s) archivé(s) le : mardi 18 avril 2017 - 22:44:18

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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〉

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