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Abstract:
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In this presentation I develop a method of bias correction, which models the error of the target estimator as a function of the corresponding bootstrap estimator, and the original estimators and bootstrap estimators of the parameters governing the model fitted to the sample data. This is achieved by considering a large number of plausible parameter values, generating a pseudo original sample for each parameter and bootstrap samples for each pseudo sample, and then searching for an appropriate functional relationship. The bias corrections are shown to be of the right order. Under certain conditions, the same procedure also permits estimation of the mean square error of the bias corrected estimator. The method is applied for estimating the prediction mean square error in small area estimation of proportions under a generalized mixed model. Empirical comparisons with the jackknife and the double bootstrap methods are presented.
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