Title :

Parametrizations, fixed and random effects

Author(s) :

Dermoune, Azzouz [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Preda, Cristian [Auteur]
MOdel for Data Analysis and Learning [MODAL]

Journal title :

Journal of Multivariate Analysis

Pages :

162 - 176

Publisher :

Elsevier

Publication date :

2016-11

ISSN :

0047-259X

English keyword(s) :

General linear model
fixed effect
random effect
cubic spline
smoothing parameter
likelihood
climate change detection

HAL domain(s) :

Statistiques [stat]/Applications [stat.AP]
Statistiques [stat]/Méthodologie [stat.ME]

English abstract : [en]

We consider the problem of estimating the random element s of a finite dimensional vector space S from the continuous data corrupted by noise with unknown variance σ 2 w. The mean E(s) (the fixed effect) of s belongs to a ...
Show more >We consider the problem of estimating the random element s of a finite dimensional vector space S from the continuous data corrupted by noise with unknown variance σ 2 w. The mean E(s) (the fixed effect) of s belongs to a known vector subspace F of S, and the likelihood of the centred component s − E(s) (the random effect) belongs to an unknown supplementary space E of F relative to S and has the PDF proportional to exp{−q(s)/2σ 2 s }, where σ 2 s is some unknown positive parameter. We introduce the notion of bases separating the fixed and random effects and define comparison criteria between two separating bases using the partition functions and the maximum likelihood method. We illustrate our results for climate change detection using the set S of cubic splines. We show the influence of the choice of separating basis on the estimation of the linear tendency of the temperature and the signal-to-noise ratio σ 2 w /σ 2 s .Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Optimisation de la prise en Charge des Patients à l'Hôpital
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL