Asymptotic theory and inference for non-stationary and non-mixing triangular arrays of random fields

Abstract

We develop a unified asymptotic framework for non-stationary, non-mixing triangular arrays of random fields on multi-dimensional lattices under row-uniform $\eta$-weak dependence. We establish the preservation of weak dependence under locally Lipschitz transformations and spatially and row-wise heterogeneous Bernoulli shifts, obtaining explicit dependence bounds determined by innovation dependence and functional sensitivity. Under uniform moment conditions, polynomially decaying $\eta$-dependence coefficients, and a nondegenerate aggregate variance condition, we prove a law of large numbers and a central limit theorem. The scope of the framework is illustrated through several examples that highlight its ability to accommodate non-stationarity without requiring mixing assumptions. As an application, we develop parameter inference procedures for a spatio-temporal model with a dynamic network structure, thereby demonstrating the practical relevance of the proposed asymptotic theory.