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.

Undergraduate research experiences (UREs), whether within the context of a mentor-mentee experience or a classroom framework, represent an excellent opportunity to expose students to the independent scholarship model. The high impact of undergraduate research has received recent attention in the context of STEM disciplines. Reflecting a 2017 survey of statistics faculty, this manuscript examines the perceived benefits of UREs, as well as barriers to the incorporation of UREs, specifically within the field of statistics. Viewpoints of students, faculty mentors, and institutions are investigated. Further, the manuscript offers several strategies for leveraging characteristics unique to the field of statistics to overcome barriers and thereby provide greater opportunity for undergraduate statistics students to gain research experience.

The U.S. Forest Inventory and Analysis Program (FIA) collects inventory data on and computes estimates for many forest attributes to monitor the status and trends of the nation's forests. Increasingly, FIA needs to produce estimates in small geographic and temporal regions. In this application, we implement area level hierarchical Bayesian (HB) small area estimators of several forest attributes for ecosubsections in the Interior West of the US. We use a remotely-sensed auxiliary variable, percent tree canopy cover, to predict response variables derived from ground-collected data such as basal area, biomass, tree count, and volume. We implement four area level HB estimators that borrow strength across ecological provinces and sections and consider prior information on the between-area variation of the response variables. We compare the performance of these HB estimators to the area level empirical best linear unbiased prediction (EBLUP) estimator and to the industry-standard post-stratified (PS) direct estimator. Results suggest that when borrowing strength to areas which are believed to be homogeneous (such as the ecosection level) and a weakly informative prior distribution is placed on the between-area variation parameter, we can reduce variance substantially compared the analogous EBLUP estimator and the PS estimator. Explorations of bias introduced with the HB estimators through comparison with the PS estimator indicates little to no addition of bias. These results illustrate the applicability and benefit of performing small area estimation of forest attributes in a HB framework, as they allow for more precise inference at the ecosubsection level.

The national forest inventory within the US has been experiencing a greater need to estimate forest attributes over smaller geographic areas than the inventory was originally designed for. Producing reliable estimates for these areas may require the use of estimation methods beyond post-stratification. Staying within the dominant design-based paradigm, this research explores how model-assisted estimation is impacted by leveraging data outside the area of interest. In particular, we compare the performance of the post-stratified estimator, the generalized regression estimator (GREG), and a modified GREG. Typically the assisting model of the modified GREG is fit over a sample comprising all of the areas of interest. Here we introduce a modified GREG, denoted as GREGORY, which gives the practitioner a high degree of flexibility in selecting the sample subset for constructing the assisting model. We use these estimators to produce county level estimates of the mean of four forest attributes in the Interior Western US. Comparing the relative efficiencies of the estimators, we find that the more complex estimators, GREG and GREGORY, generally improve the precision of the estimates, especially in regions with a high degree of forested land. When using all the data from a 10-year measurement, fitting the model over a larger region does not lead to efficiency gains. To explore the impact of smaller sample sizes, we conduct a simulation study and find that as the sampling intensity decreases, the GREGORY tends to produce more efficient estimates than the GREG, and its variance estimator exhibits less negative bias. The GREG and GREGORY can easily be computed and compared using a new R package, gregRy, available on CRAN.