On the model-assisted regression estimators using remotely sensed auxiliary data

The model-assisted difference and regression estimators are increasingly used with forest inventory and remotely sensed data to increase the precision of estimates of inventory parameters. Although these estimators date back at least 50 years and appear in multiple current sampling textbooks, the associated terminology is inconsistently defined, even among the prominent authorities. Further, two of the most prominent statistical sampling textbooks, Cochran (1977) and Sa spacing diaeresis rndal et al. (1992), use considerably different notation.The study focused on three objectives: (1) to formulate consistent and operationally useful definitions via a synthesis of the literature, (2) to construct a bridge between the more complex Sa spacing diaeresis rndal et al. (1992) notation and the more commonly used Cochran (1977) notation, and (3) to assess sample size, model form and g-weight effects on the unbiasedness of the regression estimators of both the population mean and the variance of its estimate.The data analyses entailed Monte Carlo simulations using an artificial population constructed using inventory and airborne laser scanning data and both across- and within-dataset analyses for 11 inventory datasets representing six countries on four continents. The analyses focused on assessing the unbiasedness of the regression estimators of both the mean and variance, the role of the g-weights on the unbiasedness of the variance estimator, and differences for linear versus nonlinear models. Key terminological distinctions were that the generalized estimators accommodate unequal probability sampling and that the difference estimator of the mean is unbiased whereas the regression estimator of the mean is only asymptotically unbiased, meaning it only approaches unbiasedness as the sample size increases.The key analytical conclusions were threefold: (1) the regression variance estimator was confirmed as asymptotically unbiased, (2) the form of the regression variance estimator that incorporated the g-weights was more accurate, and (3) the regression variance estimator was more accurate for linear models than for nonlinear models.