Abstract

Many small area parameters are nonlinear functions of the model response variable. A common approach to the prediction of nonlinear parameters uses simulation to approximate the empirical best predictor. We propose a general estimator of the mean square error (MSE) of predictors of nonlinear small area parameters. We estimate the leading term in the MSE, which is the MSE of the best predictor (constructed with the true parameters), using the same simulated samples used to construct the basic predictor. We then use the bootstrap to estimate the second term in the MSE, which reflects variability in the estimated parameters. We incorporate a correction for the bias of the estimator of the leading term without the use of computationally intensive double bootstrap procedures. The procedures extend readily to an informative sample design. The methods also enable the construction of calibrated prediction intervals that rely less on normal theory than standard prediction intervals. We compare the properties of several measures of uncertainty through simulations under informative and noninformative sampling. We apply the methods to predict several functions of sheet and rill erosion for Iowa counties using data from a complex agricultural survey.