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Biometrics
09, 2023;79 (3): 1880-1895.

Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space.

Ting Li, Huichen Zhu, Tengfei Li, Hongtu Zhu
Author Information
  1. Ting Li: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China.
  2. Huichen Zhu: Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong. ORCID
  3. Tengfei Li: Department of Radiology and Biomedical Research Imaging Center (BRIC), University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.
  4. Hongtu Zhu: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA. ORCID
PMID: 36205584 DOI: 10.1111/biom.13767

Abstract

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).

Keywords

Bahadur representation asynchronous longitudinal functional data functional regression kernel-weighted loss function penalized likelihood ratio test reproducing kernel Hilbert space

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MeSH Term

Humans
Linear Models
Alzheimer Disease
Computer Simulation
Algorithms
Likelihood Functions
Journal Article Research Support, Non-U.S. Gov't
Article has an altmetric score of 1

Word Cloud

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