On the effective geographic sample size

Abstract

ABSTRACTGriffith [Effective geographic sample size in the presence of spatial autocorrelation. Ann Assoc Amer Geogr. 2005;95:740–760] suggested a formula to compute the effective sample size, say , for georeferenced data. In this article, we provide mathematical support that enhances the use of this definition in practice. We prove that and that is increasing in n. We also prove the asymptotic normality of the maximum likelihood estimate of for an increasing domain sampling framework. Asymptotic normality leads to an approximate hypothesis testing that establishes whether redundant information exists in a sample.