Model-assisted estimation of domain totals, areas, and densities in two-stage sample survey designs

Model-assisted, two-stage forest survey sampling designs provide a means to combine airborne remote sensing data, collected in a sampling mode, with field plot data to increase the precision of national forest inventory estimates, while maintaining important properties of design-based inventories, such as unbiased estimation and quantification of uncertainty. In this study, we present a comprehensive set of model-assisted estimators for domain-level attributes in a two-stage sampling design, including new estimators for densities, and compare the performance of these estimators with standard poststratified estimators. Simulation was used to assess the statistical properties (bias, variability) of these estimators, with both simple random and systematic sampling configurations, and indicated that (1) all estimators were generally unbiased and (2) the use of lidar in a sampling mode increased the precision of the estimators at all assessed field sampling intensities, with particularly marked increases in precision at lower field sampling intensities. Variance estimators are generally unbiased for model-assisted estimators without poststratification, while variance estimators for model-assisted estimators with poststratification were increasingly biased as field sampling intensity decreased. In general, these results indicate that airborne remote sensing data, collected as an intermediate level of sampling, can be used to increase the efficiency of national forest inventories in remote regions.