Title :

Parametrizations, fixed and random effects

Author(s) :

Dermoune, Azzouz [Auteur]
Laboratoire Paul Painlevé [LPP]
Preda, Cristian [Auteur]
Laboratoire Paul Painlevé [LPP]

Journal title :

Journal of Multivariate Analysis

Publisher :

Elsevier

Publication date :

2016-11

ISSN :

0047-259X

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]

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

Audience :

Internationale

Popular science :

Non

Administrative institution(s) :

CNRS
Université de Lille

Collections :

• METRICS : Evaluation des technologies de santé et des pratiques médicales - ULR 2694

Submission date :

2020-06-08T14:10:40Z
2020-06-09T09:00:33Z