Regularized Spatial Downscaling in high dimensional spatial regression

Music City Center 

We consider the problem of spatial downscaling when aggregated values of the response variable and of a large number of potential covariates are observed. We show that a naïve application of standard regularization methods can lead to misleading predictions at finer resolutions. We develop a novel regularization methodology that provides dimension reduction as well as scale-adaptive predictions at finer scales with minimal computational overhead. We study theoretical properties of the method under a mixed increasing domain spatial asymptotic structure and also report results from a moderately large simulation study.

Spatial downscaling

LASSO

Spatial prediction

Mixed Increasing Domain Asymptotics