Small area estimators in a simulation test

Abstract

The Finnish National Forest Inventory produces municipality level results either with an indirect model-based K-nearest neighbor (K-NN) estimator or a direct design-based post-stratification estimator. Design-based approach is unbiased, but not always feasible due to low number of field plots. The K-NN estimator is lacking an analytical estimator for the variance. A composite estimator combining the indirect and direct estimates could be an attractive solution. In this article, estimators for small-area estimation are analyzed in a simulation experiment with varying size small areas and varying quality auxiliary data. The potential of estimators is assessed based on the true standard errors and RMSEs in the simulation experiment. Direct estimators and composite estimators work reasonably well with varying quality models, but the performance of indirect estimators is dependent on the quality of the model used. The performance of different estimators also depends on the size of the small areas. Linear models in which the weight of plots outside the target domain is smaller than those within the target domain, performed better than an unweighted model, suggesting that localizing the models for the small areas is beneficial. EBLUP approach also performed well, both in connection of a K-NN model and a linear model.