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A difficulty in MSE estimation occurs because we do not specify a fulldistribution for the survey weights. This obfuscates the use of fullyparametric bootstrap procedures. To overcome this challenge, we develop a novelMSE estimator. We estimate the leading term in the MSE, which is the MSE of thebest predictor (constructed with the true parameters), using the same simulatedsamples used to construct the basic predictor. We then exploit the asymptoticnormal distribution of the parameter estimators to estimate the second term inthe MSE, which reflects variability in the estimated parameters. We incorporatea correction for the bias of the estimator of the leading term without the useof computationally intensive double-bootstrap procedures. We further developcalibrated prediction intervals that rely less on normal theory than standardprediction intervals. We empirically demonstrate the validity of the proposedprocedures through extensive simulation studies. We apply the methods topredict several functions of sheet and rill erosion for Iowa counties usingdata from a complex agricultural survey.

Alternative Mean Square Error Estimators and Confidence Intervals for Prediction of Nonlinear Small Area Parameters