Estimating area from an accuracy assessment error matrix

A map of land cover or land-cover change produced from remotely sensed data is linked to estimation of area of land cover or land-cover change via an accuracy assessment of the map. A variety of area estimators have been proposed based on different approaches to using the estimated error matrix produced from an accuracy assessment along with information available from the map. These estimators include a stratified estimator (where the strata are the map classes), several model-assisted estimators incorporating the map information as auxiliary variables in a variety of different models, and a bias-adjusted estimator that corrects for classification error when area is computed directly from the map. In some cases the same area estimator results from more than one approach. For stratified random sampling with the map classes defining the strata, the model-assisted and bias-adjusted estimators are equivalent to the stratified estimator of area that would typically be used with this sampling design. Thus the commonly used stratified estimator is the lone choice for stratified random sampling. For simple random sampling, the bias-adjusted estimator and a model-assisted difference estimator are equivalent, but other model-assisted options include poststratified (i.e., applying a stratified estimator to data obtained from a simple random sample), ratio, and simple regression estimators. A simulation study demonstrates that for simple random sampling, the poststratified estimator almost always has the smallest variance among these estimators. The only exception to the superior performance of the poststratified estimator occurred when overall accuracy was very high, the true proportion of area was small (i.e., less than 2%), and the accuracy assessment sample size was small (n = 100). Because the poststratified estimator for simple random sampling is equivalent to the stratified estimator used with stratified random sampling, the stratified estimator provides a unified, simple approach to area estimation for these two commonly used sampling designs.