Abstract

In this paper, we propose a robust nonparametric method for learning and inferring from noisy

imaging data by modeling it as contaminated functional data, which enables accurate estimation of the

underlying signals and efficient detection and localization of significant effects. The proposed robust and

smoothed M-estimator is based on bivariate penalized splines over triangulation, effectively addressing

challenges posed by contaminated imaging data, spatial dependencies, and irregular domains commonly

encountered in imaging applications. We establish the L2 convergence of the proposed M-based mean

function estimator under certain regularity conditions and investigate its asymptotic normality. Additionally,

we present a novel approach for constructing a simultaneous confidence corridor for the mean signal of a

set of noisy imaging data. Extensive simulation studies and a real-data application with brain imaging data

illustrate the effectiveness of the proposed robust methods.

Information

Preprint No.SS-2024-0402
Manuscript IDSS-2024-0402
Complete AuthorsYang Long, Guanqun Cao, David Kepplinger, Lily Wang
Corresponding AuthorsLily Wang
Emailslwang41@gmu.edu

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Acknowledgments

Data used in the preparation of this article were obtained from the Alzheimer’s Disease

Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu). As such, the

investigators within the ADNI contributed to the design and implementation of ADNI and/or

provided data but did not participate in analysis or writing of this report. A complete listing of

ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/

uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.

The research work of Yang Long and Lily Wang is partially supported by the National

Institutes of Health award 1R01AG085616 and the National Science Foundation grant DMS-

  1. Guanqun Cao’s research is partially supported by the National Science Foundation

under Grants DMS-2413301, CNS-2319342 and CNS-2319343.

This project was further supported by resources provided by the Office of Research

Computing at George Mason University (URL: https://orc.gmu.edu) and funded in

part by grants from the National Science Foundation (Award Number 2018631).

Supplementary Materials

In the Supplementary Material, we provide additional simulation studies and detailed proofs

of the theoretical results in this paper.

Supplementary materials are available for download.