Multivariate Spline Estimation and Inference for Varying Coefficient Models with Imaging Data

• Activity Number: 603 - New Development on Statistics in Imaging
• Type: Topic Contributed
• Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Imaging
• Author(s): Shan Yu* and Guannan Wang and Li Wang and Lijian Yang
• Companies: Iowa State University and College of William and Mary and Iowa State University and Tsinghua University
• Keywords: Bivariate splines; functional linear regression; functional principal component analysis; image analysis; triangulation; uncertainty map

Abstract

Motivated by recent work of analyzing data in the biomedical imaging studies, we consider a class of spatially varying coefficient models and apply linear functional regression for imaging responses and scalar predictors. We propose to use flexible bivariate splines over triangulations to handle the irregular domain of the objects of interest on the images and other characteristics of images. The proposed spline estimators of the coefficient functions are proved to be root-n consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. Asymptotic confidence intervals and data-driven confidence corridors (CCs) for the coefficient functions are constructed. Our method can simultaneously estimate and make inferences of the coefficient functions while incorporating the spatial heterogeneity and spatial correlation. Highly efficient and scalable estimation algorithm is developed. The proposed method is applied to the spatially normalized Positron Emission Tomography (PET) data of Alzheimer's Disease Neuroimaging Initiative (ADNI).