Spatial effect detection regression for large-scale spatio-temporal covariates

Abstract We develop a Spatial Effect Detection Regression (SEDR) model to capture the nonlinear and irregular effects of high-dimensional spatio-temporal predictors on a scalar outcome. Specifically, we assume that both the component and the coefficient functions in the SEDR are unknown smooth functions of location and time. This allows us to leverage spatially and temporally correlated information, transforming the curse of dimensionality into a blessing, as confirmed by our theoretical and numerical results. Moreover, we introduce a set of 0–1 regression coefficients to automatically identify the boundaries of the spatial effect, implemented via a novel penalty. A simple iterative algorithm, with explicit forms at each update step, is developed, and we demonstrate that it converges from the initial values given in the paper. Furthermore, we establish the convergence rate and selection consistency of the proposed estimator under various scenarios involving dimensionality and the effect space. Through simulation studies, we thoroughly evaluate the superior performance of our method in terms of bias and empirical efficiency. Finally, we apply the method to analyse and forecast data from environmental monitoring and Alzheimer’s Disease Neuroimaging Initiative study, revealing interesting findings and achieving smaller out-of-sample prediction errors compared to existing methods.