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

TL;DR

This paper introduces a bootstrap-weighted k-Nearest-Neighbor method to create realistic artificial populations for evaluating small area estimators in forest inventories, enabling more accurate model comparison without ground truth.

Contribution

It proposes a novel KBAABB method combining kNN and ABB techniques for generating artificial populations for SAE evaluation, with diagnostic checks and practical application to US forest data.

Findings

KBAABB produces realistic artificial populations for SAE assessment.

The method allows effective comparison of SAE models without ground truth.

Application to US forest data demonstrates practical utility.

Abstract

National Forest Inventories (NFIs) 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 NFIs 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 (ABB), and k Nearest Neighbor (kNN) imputation methods to propose a kNN-based approximation to ABB (KBAABB), for generating an artificial population when rich unit-level auxiliary data is available. We introduce diagnostic checks on the process of building the artificial population, and we demonstrate how to use such an artificial population for design-based simulation studies to compare and evaluate SAE models, using real data from the United States Department of Agriculture, Forest Service, Forest Inventory and Analysis Program, the NFI of the United States.