Comparison Study of the Generalized Multivariate Difference Estimator and the Generalized Regression Estimator
The Forest Inventory and Analysis (FIA) Program of the U.S. Forest Service commonly uses estimators from the Generalized Regression Estimator (GREG) family to estimate forest attributes. The GREG combines complex survey data and auxiliary data, such as remote-sensing data, to produce more precise estimates. Meanwhile, a similar estimator, the Generalized Multivariate Difference Estimator (GMDE) also combines complex survey data and auxiliary data. The key difference between the GREG and the GMDE is the optimization goal when combining these data sources: GREG seeks to find the best coefficient estimates for a model between the survey data and the auxiliary data while the GMDE focuses on optimal coefficients of a linear transformation of the Horvitz–Thompson estimator. Additionally, the GMDE allows several study variables to be estimated at the same time. The GREG is widely used by FIA while its similar counterpart, the GMDE is not. In our research, we’ve made both analytical and computational comparisons of the two estimators and shown the merits of the GMDE. We have investigated not only how the two approaches are related, but also when one is more applicable than the other under different sampling designs.