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

页码：24 / 41

页数：18

共 50 条

[1] Wavelet penalized likelihood estimation in generalized functional models
Gannaz, Irene
[J]. TEST, 2013, 22 (01) : 122 - 158
[2] Wavelet penalized likelihood estimation in generalized functional models
Irène Gannaz
[J]. TEST, 2013, 22 : 122 - 158
[3] Penalized empirical likelihood for generalized linear models with longitudinal data
Tan, Xiaoyan
Yan, Li
[J]. COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2021, 50 (02) : 608 - 623
[4] Penalized contrast estimation in functional linear models with circular data
Brunel, E.
Roche, A.
[J]. STATISTICS, 2015, 49 (06) : 1298 - 1321
[5] Penalized empirical likelihood for high-dimensional generalized linear models with longitudinal data
Chen, Xia
Tan, Xiaoyan
Yan, Li
[J]. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2023, 93 (10) : 1515 - 1531
[6] Penalized quasi-likelihood estimation in partial linear models
Mammen, E
Van de Geer, S
[J]. ANNALS OF STATISTICS, 1997, 25 (03): : 1014 - 1035
[7] Estimation and variable selection via frailty models with penalized likelihood
Androulakis, E.
Koukouvinos, C.
Vonta, F.
[J]. STATISTICS IN MEDICINE, 2012, 31 (20) : 2223 - 2239
[8] Penalized empirical likelihood for high-dimensional generalized linear models
Chen, Xia
Mao, Liyue
[J]. STATISTICS AND ITS INTERFACE, 2021, 14 (02) : 83 - 94
[9] Penalized log-likelihood estimation for partly linear transformation models with current status data
Ma, SG
Kosorok, MR
[J]. ANNALS OF STATISTICS, 2005, 33 (05): : 2256 - 2290
[10] Tuning Parameter Selector for the Penalized Likelihood Method in Multivariate Generalized Linear Models
Wang, Xiaoguang
Song, Lixin
Cui, Jie
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2013, 42 (21) : 3873 - 3888

← 1 2 3 4 5 →