Topics in small area estimation with applications to the National Resources Inventory

A practical application of small area estimation in the National Resources Inventory, a large survey of the non-federal land area in the United States, is described. Several estimation issues raised by this application are discussed as motivation for theoretical investigation of some aspects of small area estimation;The situation in which individual small area sampling variances are directly estimated is studied. This situation is not covered by standard asymptotic results (Prasad and Rao (1990)), which assume that a finite-dimensional parameter characterizes the small area variances. An approximation for the mean square error (MSE) of the empirical best linear unbiased predictor and an estimator of the MSE are developed. Simulation studies show that the theoretical expressions are good approximations for the MSE of the predictors. Also the suggested MSE estimator has smaller overestimation for the MSE than related estimators in the literature when the between-area variance component is small;Small area estimation under a restriction, which forces small area estimates to sum to the direct estimate for a large area, is discussed. A criterion that unifies the derivation of several restricted estimators is proposed. The estimator that is the unique best linear unbiased estimator under the criterion is derived and an approximation for the MSE of the restricted estimator is presented;The bias of the empirical best linear unbiased predictor is assessed for the model in which the sampling errors are not normally distributed. The robustness of the MSE estimator is examined under non-normal error distributions by using simulations. The simulations also demonstrate that imposing a restriction can reduce the bias when the errors are not symmetrically distributed