A Comparison of Model-Assisted Estimators, With and Without Data-Driven Transformations of Auxiliary Variables, With Application to Forest Inventory

Abstract

Forest information is requested at many levels and for many purposes. Sampling-based national forest inventories (NFIs) can provide reliable estimates on national and regional levels. By combining expensive field plot data with different sources of remotely sensed information, from airplanes and/or satellite platforms, the precision in estimators of forest variables can be improved. This paper focuses on the design-based model-assisted approach to using NFI data together with remotely sensed data to estimate forest variables for small areas, where the variables studied are total growing stock volume, volume of Norway spruce (Picea abies), and volume of broad-leaved trees. Remote sensing variables may be highly correlated with one another and some may have poor predictive ability for target forest variables, and therefore model selection and/or coefficient shrinkage may be appropriate to improve the efficiency of model-assisted estimators of forest variables. For this purpose, one can use modern shrinkage estimators based on lasso, ridge, and elastic net regression methods. In a simulation study using real NFI data, Sentinel 2 remote-sensing data, and a national airborne laser scanning (ALS) campaign, we show that shrinkage estimators offer advantages over the (weighted) ordinary least-squares (OLS) estimator in a model-assisted setting. For example, for a sample size n of about 900 and with 72 auxiliary variables, the RMSE was up to 41% larger when based on OLS. We propose a data-driven method for finding suitable transformations of auxiliary variables, and show that it can improve estimators of forest variables. For example, when estimating volume of Norway spruce, using a smaller expert selection of auxiliary variables, transformations reduced the RMSE by up to 10%. The overall best results in terms of RMSE were obtained using shrinkage estimators and a larger set of 72 auxiliary variables. However, for this larger set of variables, the use of transformations yielded at most small improvements of RMSE, and at worst large increases of RMSE, except in combination with ridge and elastic net regression.