Benchmarked Small Area Prediction

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  • Author: Emily Berg and Wayne A. Fuller
  • Date: 03 April 2019
  • Copyright: Image copyright of Patrick Rhodes

Small area estimation often involves constructing predictions with an estimated model followed by a benchmarking step. In the benchmarking operation, the predictions are modified so that weighted sums satisfy constraints. The most common constraint is the constraint that a weighted sum of predictions is equal to the same weighted sum of the original observations. Two benchmarking procedures for nonlinear models are proposed in a paper published in The Canadian Journal of Statistics: a linear additive adjustment and a method based on an augmented model for the expectation function. Variance estimators for benchmarked predictors are presented and vetted through simulation studies. The benchmarking procedures are applied to county estimates of the proportion of area in cropland using data from the National Resources Inventory.

Benchmarked small area prediction

Emily Berg and Wayne A. Fuller

The Canadian Journal of Statistics, Volume 46, Issue 3, September 2018, pages 482-500

The paper is available via the link above and the authors explain their findings in further detail below.

thumbnail image: Benchmarked Small Area Prediction

The National Resources Inventory, a longitudinal survey of land cover and land use in the United States, publishes estimates at national, regional, and state levels. In particular, the NRI publishes an estimate of the proportion of each state classified as cropland. An estimate of the proportion of each county classified as cropland is not published, but county level estimates are of interest to data users. The NRI county estimation problem is a specific case of small area estimation, a general class of problems in which estimates are required for domains that are smaller than the originally planned estimation domains. Standard survey estimators for small areas are often unreliable because of small sample sizes at the area level. Small area estimation incorporates auxiliary information through statistical models, where auxiliary information is from sources external to the survey of interest. The use of auxiliary information combined with a model can lead to small area predictors that are more efficient than standard survey estimators for the small domains of interest. The models are most effective if the auxiliary variables are strongly correlated with the survey outcomes of interest. In the NRI application, the Cropland Data Layer (CDL) provides auxiliary information. The CDL contains a land cover classification for 30x30 meter pixels based on satellite imagery. Due to differences in definitions and measurement procedures, the CDL classification is not identical to the NRI classification, but the two measurements of the area in cropland at the county level are strongly correlated. A practical challenge in small area estimation occurs when model based small area predictors are aggregated to a larger domain for which estimates have been published. The simple weighted sum of model based small area predictors can differ from an existing published estimate. In the NRI application, the sum of model based estimates of cropland area for counties in a state may not equal the published state level estimate. A procedure known as benchmarking forces specified weighted sums of model based estimates to equal the previously published value. This paper investigates benchmarking procedures for nonlinear models. The benchmarking procedures are applied to estimate the proportion of county area that is cropland for Minnesota counties.

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