The Annals of Applied Statistics

Regularized 3D functional regression for brain image data via Haar wavelets

Xuejing Wang, Bin Nan, Ji Zhu, and Robert Koeppe

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The primary motivation and application in this article come from brain imaging studies on cognitive impairment in elderly subjects with brain disorders. We propose a regularized Haar wavelet-based approach for the analysis of three-dimensional brain image data in the framework of functional data analysis, which automatically takes into account the spatial information among neighboring voxels. We conduct extensive simulation studies to evaluate the prediction performance of the proposed approach and its ability to identify related regions to the outcome of interest, with the underlying assumption that only few relatively small subregions are truly predictive of the outcome of interest. We then apply the proposed approach to searching for brain subregions that are associated with cognition using PET images of patients with Alzheimer’s disease, patients with mild cognitive impairment and normal controls.

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Ann. Appl. Stat., Volume 8, Number 2 (2014), 1045-1064.

First available in Project Euclid: 1 July 2014

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Alzheimer’s disease brain imaging functional data analysis Haar wavelet Lasso PET image variable selection


Wang, Xuejing; Nan, Bin; Zhu, Ji; Koeppe, Robert. Regularized 3D functional regression for brain image data via Haar wavelets. Ann. Appl. Stat. 8 (2014), no. 2, 1045--1064. doi:10.1214/14-AOAS736.

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Supplemental materials

  • Supplementary material: Appendix. The online supplementary material contains the technical appendix showing the theoretical results of the proposed approach and an illustrative example showing the desirable feature of Haar wavelets.