In forest inventories, regression models are often applied to predict quantities such as biomass at the level of sampling units. In this paper, we propose a model-based inference framework for combining sampling and model errors in the variance estimation. It was applied to airborne laser (LiDAR) data sets from Hedmark County, Norway, where the model error proportion of the total variance was found to be large for both scanning (airborne laser scanning) and profiling LiDAR when biomass was estimated. With profiling LiDAR, the model error variance component for the entire county was as large as 71% whereas for airborne laser scanning, it was 43% of the total variance. Partly, this reflects the better accuracy of the pixel-based regression models estimated from scanner data as compared with the models estimated from profiler data. The framework proposed in our study can be applied in all types of sample surveys where model-based predictions are made at the level of individual sampling units. Especially, it should be useful in cases where model-assisted inference cannot be applied due to the lack of a probability sample from the target population or due to problems of correctly matching observations of auxiliary and target variables.
Parallel Processing of Airborne Laser Scanning Data Using a Hybrid Model Based on MPI and OpenMP
