Estimation of the mean function of functional data via deep neural networks
Document Type
Article
Publication Date
12-1-2021
Abstract
In this work, we propose a deep neural networks-based method to perform non-parametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with rectifier linear unit (ReLU) activation function. We provide the convergence rate of the proposed deep neural networks estimator in terms of the empirical norm. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyse positron emission tomography images of patients with Alzheimer's disease obtained from the Alzheimer Disease Neuroimaging Initiative database.
Identifier
85112743280 (Scopus)
Publication Title
Stat
External Full Text Location
https://doi.org/10.1002/sta4.393
e-ISSN
20491573
Issue
1
Volume
10
Grant
W81XWH‐12‐2‐0012
Fund Ref
Alzheimer's Disease Neuroimaging Initiative
Recommended Citation
Wang, Shuoyang; Cao, Guanqun; and Shang, Zuofeng, "Estimation of the mean function of functional data via deep neural networks" (2021). Faculty Publications. 3607.
https://digitalcommons.njit.edu/fac_pubs/3607