Abstract

Motivated by imaging genetics, this paper introduces a semi-nonparametric

varying coefficients modeling framework to reveal varying associations between

genetic markers and imaging responses.

We aim to conduct a comprehensive

theoretical analysis of estimation and inference procedures applicable to these

models. By employing the kernel machine method, we estimate unknown varying coefficient functions and derive their representer theorem. We also establish

the theoretical properties of these estimated functions, including their rate of convergence, Bahadur representation, point-wise limit distributions, and confidence

intervals. Additionally, we propose test statistics under a linear mixed effects

model framework to assess the significance of all varying coefficients, taking into

account within-subject dependence. The efficacy of our proposed methodology

is demonstrated through simulation studies and an application to data from the

Alzheimer’s Disease Neuroimaging Initiative study.

Information

Preprint No.SS-2024-0118
Manuscript IDSS-2024-0118
Complete AuthorsTing Li, Yang Yu, Xiao Wang, J.S. Marron, Hongtu Zhu
Corresponding AuthorsHongtu Zhu
Emailshtzhu@email.unc.edu

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Acknowledgments

Dr. Zhu’s work was partially supported by the Gillings Innovation Laboratory

on generative AI and by grants from the National Institute on Aging (NIA) of the

National Institutes of Health (NIH), including 1R01AG085581, and RF1AG082938,

the National Institute of Mental Health (NIMH) grant 1R01MH136055, and the

NIH grants R01AR082684, and 1OT2OD038045-01. The content is solely the

responsibility of the authors and does not necessarily represent the official views

of the National Institutes of Health.

Supplementary Materials

Additional simulation results, additional real data analysis, and details of

all the proofs can be found in the supplementary material.

Supplementary materials are available for download.