A method for empirically assessing small area estimators via bootstrap-weighted k-nearest-neighbor artificial populations, with applications to forest inventory

National Forest Inventories monitor forest attributes across a variety of spatial and temporal scales in a given country. Increased interest in reporting and management at smaller scales has driven National Forest Inventories to investigate and adopt small area estimation (SAE) due to the promise of increased precision at these scales. However, comparing and evaluating SAE models for a given application is inherently difficult. Typically, many areas lack enough data to check unit-level modeling assumptions or to assess unit-level predictions empirically; and no ground truth is available for checking area-level estimates. Design-based simulation from artificial populations can help with each of these issues, but only if the artificial populations realistically represent the application at hand and are not built using assumptions that inherently favor one SAE model over another. In this paper, we borrow ideas from random hot deck, approximate Bayesian bootstrap, and $k$ nearest neighbor imputation methods to propose a $k$ nearest neighbor-based approximation to approximate Bayesian bootstrap, for generating an artificial population when rich unit-level auxiliary data are available. We introduce diagnostic checks on the process of building the artificial population, and demonstrate how to use it for design-based simulation studies to compare and evaluate SAE models, using real data from the Forest Inventory and Analysis program of the United States Department of Agriculture Forest Service (the National Forest Inventory of the United States).