Assessing components of the model-based mean square error estimator for remote sensing assisted forest applications

Model-based inference is an alternative to probability-based inference for small areas or remote areas for which probability sampling is difficult. Model-based mean square error estimators incorporate three components: prediction covariance, residual variance, and residual covariance. The latter two components are often considered negligible, particularly for large areas, but no thresholds that justify ignoring them have been reported. The objectives of the study were threefold: (i) to compare analytical and bootstrap estimators of model parameter covariances as the primary factors affecting prediction covariance; (ii) to estimate the contribution of residual variance to overall variance; and (iii) to estimate thresholds for residual spatial correlation that justify ignoring this component. Five datasets were used, three from Europe, one from Africa, and one from North America. The dependent variable was either forest volume or biomass and the independent variables were either Landsat satellite image bands or airborne laser scanning metrics. Three conclusions were noteworthy: (i) analytical estimators of the model parameter covariances tended to be biased; (ii) the effects of residual variance were mostly negligible; and (iii) the effects of spatial correlation on residual covariance vary by multiple factors but decrease with increasing study area size. For study areas greater than 75 km² in size, residual covariance could generally be ignored.