Estimation in generalized linear models for functional data via penalized likelihood

被引：94
|
作者：
Cardot, H
Sarda, P
机构：
[1] INRA Toulouse, Unite Biometrie & Intelligence Artificielle, F-31326 Castanet Tolosan, France
[2] Univ Toulouse 3, Lab Stat & Probabil, F-31062 Toulouse, France
来源：
JOURNAL OF MULTIVARIATE ANALYSIS | 2005年 / 92卷 / 01期
关键词：
covariance operator; Hilbert space valued random variables; III-posed problem; regularization; splines;
D O I：
10.1016/j.jmva.2003.08.008
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We analyze in a regression setting the link between a scalar response and a functional predictor by means of a Functional Generalized Linear Model. We first give a theoretical framework and then discuss identifiability of the model. The functional coefficient of the model is estimated via penalized likelihood with spline approximation. The L(2) rate of convergence of this estimator is given under smoothness assumption on the functional coefficient. Heuristic arguments show how these rates may be improved for some particular frameworks. (C) 2003 Elsevier Inc. All rights reserved.
引用
收藏
页码：24 / 41
页数：18
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