On the effective geographic sample size

ABSTRACT

Griffith [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 $n^{\ast }$, for georeferenced data. In this article, we provide mathematical support that enhances the use of this definition in practice. We prove that $n^{\ast }\in [1,n]$ and that $n^{\ast }$ is increasing in n. We also prove the asymptotic normality of the maximum likelihood estimate of $n^{\ast }$ for an increasing domain sampling framework. Asymptotic normality leads to an approximate hypothesis testing that establishes whether redundant information exists in a sample.

Keywords:

• Covariance function
• Gaussian process
• spatial regression model
• increasing domain
• hypothesis testing

Acknowledgements

Daniel A. Griffith is an Ashbel Smith Professor of Geospatial Information Sciences at the University of Texas at Dallas.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

AC3E stands for Advanced Center for Electrical and Electronic Engineering, UTFSM, grant FB-0008.