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Nonparametric random effects functional regression model using Gaussian process priors

Lookup NU author(s): Dr Jian Shi

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Abstract

© 2021 Institute of Statistical Science. All rights reserved.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.

Publication metadata

Author(s): Wang Z, Ding H, Chen Z, Shi JQ

Publication type: Article

Publication status: Published

Journal: Statistica Sinica

Year: 2021

Volume: 31

Issue: 1

Pages: 53-78

Online publication date: 01/01/2021

Acceptance date: 02/04/2018

ISSN (electronic): 1017-0405

Publisher: Institute of Statistical Science

URL: https://doi.org/10.5705/SS.202018.0296

DOI: 10.5705/ss.202018.0296

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