Parametrizations, fixed and random effects

详细信息    查看全文

• 作者：Azzouz Dermoune^a ; ^{azzouz.dermoune@univ-lille1.fr} ; Cristian Preda^a ; ^b ; ^c ; ^{cristian.preda@polytech-lille.fr}
• 关键词：62G05 ; 62J02 ; 62G08
• 刊名：Journal of Multivariate Analysis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：154
• 期：Complete
• 页码：162-176
• 全文大小：1171 K
• 卷排序：154

文摘

We consider the problem of estimating the random element s of a finite-dimensional vector space SS from the continuous data corrupted by noise with unknown variance σw2. It is assumed that the mean E(s) (the fixed effect) of s belongs to a known vector subspace FF of SS, and that the likelihood of the centered component s−E(s) (the random effect) belongs to an unknown supplementary space EE of FF relative to SS. Furthermore, the likelihood is assumed to be proportional to exp{−q(s)/2σs2}, where σs2 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 SS 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 σw2/σs2.