Spatio-Temporal Expanding Distance Asymptotic Framework for Locally Stationary Processes

Abstract

Spatio-temporal data indexed by sampling locations and sampling time points are encountered in many scientific disciplines such as climatology, environmental sciences, and public health. Here, we propose a novel spatio-temporal expanding distance (STED) asymptotic framework for studying the properties of statistical inference for nonstationary spatio-temporal models. In particular, to model spatio-temporal dependence, we develop a new class of locally stationary spatio-temporal covariance functions. The STED asymptotic framework has a fixed spatio-temporal domain for spatio-temporal processes that are globally nonstationary in a rescaled fixed domain and locally stationary in a distance expa..