Abstract

In this paper, within a spatial statistics framework, we present an upper bound for the effective sample size (ESS) as defined by Vallejos and Osorio (2014), addressing a research gap regarding the mathematical properties of the ESS. There are certain correlation structures for which the ESS exceeds n, which is inconsistent with the maximum possible sample size. Our approach identifies conditions on the correlation matrix of a spatial process that ensure that the equivalent number of independent and identically distributed observations within a spatial sample of size n does not exceed n. This property is desirable because it ensures the effectiveness of reduction measures. © 2024 Elsevier B.V.