Sampling Designs for Estimating Spatial Variance Components

A. N. Pettitt and A. B. McBRATNEY

Journal of the Royal Statistical Society Series C, 1993, vol. 42, issue 1, 185-209

Abstract: Sampling designs and estimation procedures are considered for the spatial variogram when no information on magnitude or scale of variation of a spatial variable is available. Design‐based solutions to this problem have involved nested balanced designs and estimation based on the method of moments for a random effects model. It has been suggested that highly unbalanced staggered designs may be more efficient in terms of sampling effort than balanced nested designs. All the previous methods based on the estimation of variance components are essentially non‐spatial, however. Practical, spatial and parsimonious considerations lead us to a hybrid design–model‐based approach of staggered designs on linear transects in three orientations as a suitable sampling procedure. Estimation of the parameters of the accompanying variance components model is done by restricted maximum likelihood (REML) and ML. The REML estimates approximate the spatial variogram over several orders of magnitude. All methods are illustrated with soil survey data and extensive data analysis is carried out. A set of data is given in the appendix.

Date: 1993
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