Small area estimation of forest biomass via a two-stage model for continuous zero-inflated data

Nationwide Forest Inventories (NFIs) collect data on and monitor the trends of forests across the globe. Users of NFI data are increasingly interested in monitoring forest attributes such as biomass at fine geographic and temporal scales, resulting in a need for assessment and development of small area estimation techniques in forest inventory. We implement a small area estimator and parametric bootstrap estimator that account for zero-inflation in biomass data via a two-stage model-based approach and compare the performance to a Horvitz-Thompson estimator, a post-stratified estimator, and to the unit- and area-level empirical best linear unbiased prediction (EBLUP) estimators. We conduct a simulation study in Nevada with data from the United States NFI, the Forest Inventory & Analysis Program, and remote sensing data products. Results show the zero-inflated estimator has the lowest relative bias and the smallest empirical root mean square error. Moreover, the 95% confidence interval coverages of the zero-inflated estimator and the unit-level EBLUP are more accurate than the other two estimators. To further illustrate the practical utility, we employ a data application across the 2019 measurement year in Nevada. We introduce the R package, saeczi, which efficiently implements the zero-inflated estimator and its mean squared error estimator.