An approximate best prediction approach to small area estimation for sheet and rill erosion under informative sampling

Abstract

The National Resources Inventory, a longitudinal survey of characteristics related to natural resources and agriculture on nonfederal U.S. land, has increasingly received requests for substate estimates in recent years. We consider estimation of erosion in subdomains of the Boone-Raccoon River Watershed. This region is of interest for its proximity to intensively cropped areas as well as important waterbodies. The NRI application requires a small area prediction approach that can handle nonlinear relationships and appropriately incorporate survey weights that may have nontrivial relationships to the response variable. Because of the informative design, the conditional distribution required to define a standard empirical Bayes predictor is unknown. We develop a prediction approach that utilizes the approximate distribution of survey weighted score equations arising from a specified two-level superpopulation model. We apply the method to construct estimates of mean erosion in small watersheds. We investigate the robustness of the procedure to an assumption of a constant dispersion parameter and validate the properties of the procedure through simulation.