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

Abstract

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.

A design-based assessment of an expanded set of auxiliary information for forest growth estimation

“…We observe potential evidence for overestimation in RE due to the modest underestimation of the asymptotic variance estimator which becomes more pronounced as the number of selected variables increases with respect to n 2 . In an operational setting, it is recommended to address this variance underestimation either by applying a variant of the g-weight variance estimator or by bootstrapping (see McConville et al (2020) for full discussion in the finite population case). However, none of these options was feasible for this case study due to the lack of availability of certain auxiliary variables on the full first-phase grid.…”

Use of Remote Sensing Data to Improve the Efficiency of National Forest Inventories: A Case Study from the United States National Forest Inventory

“…115-334, section 8632), commonly referred to as the 2018 Farm Bill), explicitly directs the USDA Forest Service (USFS) to find efficiencies in its NFI program through the use of advanced technologies such as RS and to engage other stakeholders in these efforts. The Forest Inventory and Analysis (FIA) program, which executes the NFI, has gained efficiencies and created new products for decades through careful investments in technologies like RS [9][10][11].…”

“…The specific mathematical linkages between post-stratified and regression estimation can be seen in Bethlehem and Keller [44], Breidt and Opsomer [45], and Stehman [46]. In addition, McConville et al [11] provide a tutorial on model-assisted inference for forest inventory that presents post-stratification as a special case of a generalized regression estimator.…”

Estimating Land Use and Land Cover Change in North Central Georgia: Can Remote Sensing Observations Augment Traditional Forest Inventory Data?

“…Our status, net change, and transitional change parameters are all population means (proportions and percentages being special cases of a mean) and can therefore be estimated with any design-based estimator of a mean. Auxiliary data, denoted by x t,i for unit i at time t, which are known for both the sample and the population units, may also be brought in to improve precision in estimates through numerous model-assisted methodologies [30]. Note that the auxiliary data may or may not vary with time.…”