Can Measurement Errors Be Characterized from Replicates?

Abstract

Sample measurements (of grade, depth, etc.) are almost inevitably affected by errors. Several error models were studied in the literature. But the interest of replicates for selecting the error model received limited attention. If measurement errors are supposed to be additive, homoscedastic, without correlation between them, and spatially not correlated with the exact values, the variances of the measurement errors are computable from the sample, simple, and cross-variograms of replicate data sets, even if the variogram of the exact value is pepitic (Aldworth W, Spatial prediction, spatial sampling, and measurement error. Retrospective Theses and Dissertations. Paper 11842. Iowa State University Digital Repository @ Iowa State University, 1998; Faucheux et al. Characterisation of a hydrocarbon polluted soil by an intensive multi-scale sampling. Geostats 2008, proceedings of the 8th international geostatistics congress, 1-5 Dec. 2008, Santiago, Chile. Ortiz J-M, Emery X (eds) for an example, 2008). But what about the other cases? When the error is additive, its correlation with the exact value can remain undetectable. The variance of the measurement errors is thus not always computable. It's the same for an error of multiplicative type. Except in some special cases, keeping the different measurement values rather than their average improves the precision of the estimation.