Generalized and synthetic regression estimators for randomized branch sampling

In felled-tree studies, ratio and regression estimators are commonly used to convert more readily measured branch characteristics to dry crown mass estimates. In some cases, data from multiple trees are pooled to form these estimates. This research evaluates the utility of both tactics in the estimation of crown biomass following randomized branch sampling (RBS). Synthetic generalized regression (GREG) estimators are developed, and their properties examined against standard estimators. It is shown that synthetic GREG estimators with zero or low design-bias can be obtained, and that the variance of a design-unbiased class of GREG estimators can be unbiasedly estimated. Simulated sampling from 20 censused crowns of two Rocky Mountain species indicated that improvements in accuracy can be obtained through GREG estimation following RBS. Simulations also showed that synthetic GREG estimators that pool data from multiple trees can stabilize coefficients of multivariate regression models to provide improved accuracy over direct GREG estimators. However, for the univariate regression models that proved most adept for the censused crowns, direct GREG estimation provided the lowest average root mean squared error (RMSE) for RBS. Simulations also showed that model-based branch aggregation estimators have generally low RMSE but can be heavily design-biased. For the crown forms studied, use of branch auxiliary information at both the design and estimation stages through RBS and GREG estimation appears to be more efficient than using the information only at the estimation stage following simple or stratified random sampling.