NONPARAMETRIC RANDOM EFFECTS FUNCTIONAL REGRESSION MODEL USING GAUSSIAN PROCESS PRIORS

被引：2

作者：

Wang, Zhanfeng ^{[1
]}

Ding, Hao ^{[1
]}

Chen, Zimu ^{[1
]}

Shi, Jian Qing ^{[2
]}

机构：

[1] Univ Sci & Technol China, Dept Stat & Finance, Sch Management, Hefei, Anhui, Peoples R China

[2] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne, Tyne & Wear, England

来源：

STATISTICA SINICA | 2021年 / 31卷 / 01期

关键词：

Functional linear model; function-on-function regression model; Gaussian process priors; nonlinear random effects; ON-FUNCTION REGRESSION; LINEAR-REGRESSION;

D O I：

10.5705/ss.202018.0296

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：

For functional regression models with functional responses, we propose a nonparametric random-effects model using Gaussian process priors. The proposed model captures the heterogeneity nonlinearly and the covariance structure nonparametrically, enabling longitudinal studies of functional data. The model also has a flexible form of mean structure. We develop a procedure to estimate the unknown parameters and calculate the random effects nonparametrically. The procedure uses a penalized least squares regression and a maximum a posterior estimate, yielding a more accurate prediction. The statistical theory is discussed, including information consistency. Simulation studies and two real-data examples show that the proposed method performs well.

引用

页码：53 / 78

页数：26