A Tutorial on Model-Assisted Estimation with Application to Forest Inventory

National forest inventories in many countries combine expensive ground plot data with remotely-sensed information to improve precision in estimators of forest parameters. A simple post-stratified estimator is often the tool of choice because it has known statistical properties, is easy to implement, and is intuitive to the many users of inventory data. Because of the increased availability of remotely-sensed data with improved spatial, temporal, and thematic resolutions, there is a need to equip the inventory community with a more diverse array of statistical estimators. Focusing on generalized regression estimators, we step the reader through seven estimators including: Horvitz Thompson, ratio, post-stratification, regression, lasso, ridge, and elastic net. Using forest inventory data from Daggett county in Utah, USA as an example, we illustrate how to construct, as well as compare the relative performance of, these estimators. Augmented by simulations, we also show how the standard variance estimator suffers from greater negative bias than the bootstrap variance estimator, especially as the size of the assisting model grows. Each estimator is made readily accessible through the new R package, mase. We conclude with guidelines in the form of a decision tree on when to use which an estimator in forest inventory applications.