This study introduces five facets that can improve inference in small area estimation (SAE) problems: (1) model groups, (2) test of area effects, (3) conditional EBLUPs, (4) model selection, and (5) model averaging. Two contrasting case studies with data from the Swiss and Norwegian national forest inventories demonstrate the five facets. The target variable of interest was mean stem volume per hectare on forested land in 108 Swiss forest districts (FD) and in 14 Norwegian municipalities (KOM) in the County of Vestfold. Auxiliary variables from airborne laser scanning (Switzerland) and photogrammetric point clouds (Vestfold) with full coverage and a resolution of 25 m × 25 m (Switzerland) and 16 m × 16 m (Vestfold) were available. Only the data metric mean canopy height was statistically significant. Ten linear fixed-effects models and three mixed linear models were assessed. Area effects were statistically significant in the Swiss case but not in Vestfold case. A model selection based on AIC favored separate linear regression models for each FD and a single common regression model in Vestfold. Model averaging increased, on average, an estimated variance by 15%. Reported estimates of uncertainty were consistently larger than corresponding unconditional EBLUPs.
Small Area Estimation with Penalty for Specific Area Effects Selection
