Effective Sample Size with the Bivariate Gaussian Common Component Model

Letícia Ellen Dal Canton (), Luciana Pagliosa Carvalho Guedes, Miguel Angel Uribe-Opazo () and Tamara Cantu Maltauro
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Letícia Ellen Dal Canton: Engineering, Mathematics and Technology Department, Western Paraná State University (Universidade do Oeste do Paraná, UNIOESTE), Cascavel 85819-110, Brazil
Luciana Pagliosa Carvalho Guedes: Engineering, Mathematics and Technology Department, Western Paraná State University (Universidade do Oeste do Paraná, UNIOESTE), Cascavel 85819-110, Brazil
Miguel Angel Uribe-Opazo: Engineering, Mathematics and Technology Department, Western Paraná State University (Universidade do Oeste do Paraná, UNIOESTE), Cascavel 85819-110, Brazil
Tamara Cantu Maltauro: Engineering, Mathematics and Technology Department, Western Paraná State University (Universidade do Oeste do Paraná, UNIOESTE), Cascavel 85819-110, Brazil

Stats, 2023, vol. 6, issue 4, 1-18

Abstract: Effective sample size (ESS) consists of an equivalent number of sampling units of a georeferenced variable that would produce the same sampling error, as it considers the information that each georeferenced sampling unit contains about itself as well as in relation to its neighboring sampling units. This measure can provide useful information in the planning of future georeferenced sampling for spatial variability experiments. The objective of this article was to develop a bivariate methodology for ESS ( E S S b i ), considering the bivariate Gaussian common component model (BGCCM), which accounts both for the spatial correlation between the two variables and for the individual spatial association. All properties affecting the univariate methodology were verified for E S S b i using simulation studies or algebraic methods, including scenarios to verify the impact of the BGCCM common range parameter on the estimated E S S b i values. E S S b i was applied to real organic matter (OM) and sum of bases (SB) data from an agricultural area. The study found that 60% of the sample observations of the OM–SB pair contained spatially redundant information. The reduced sample configuration proved efficient by preserving spatial variability when comparing the original and reduced OM maps, using SB as a covariate. The Tau concordance index confirmed moderate accuracy between the maps.

Keywords: bivariate spatial process; geostatistics; Monte Carlo simulation; spatial autocorrelation (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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