Multivariate Spline Estimation and Inference for Image-on-Scalar Regression

Motivated by recent data analyses in biomedical imaging studies, we consider a class of image-on-scalar regression models for responses and scalar predictors. We propose using flexible multivariate splines over triangulations to handle the irregular domain objects interest on images, as well other characteristics images. The proposed estimators coefficient functions are proved be root-n consistent asymptotically normal under some regularity conditions. also provide computationally efficient estimator covariance function. Asymptotic pointwise confidence intervals data-driven simultaneous corridors constructed. Our method can simultaneously estimate make inferences while incorporating spatial heterogeneity correlation. A highly scalable estimation algorithm is developed. Monte Carlo simulation studies conducted examine finite-sample performance method, which then applied spatially normalized positron emission tomography Alzheimer's Disease Neuroimaging Initiative.