Purpose:To consider model-based prediction of a finite population total when a monotone transformation of a survey variable makes it appropriate to assume additive, homoscedastic errors.Summary:The transformation used does not necessarily simultaneously produce an easily parametrized mean function. Hence it is assumed that the mean is a smooth function of the auxiliary variable, and it is estimated nonparametrically. However the back transformation introduces bias, which is removed using smearing. An asymptotic expansion is obtained for prediction error, which shows its asymptotic negligibility and this prediction MSE has the same order as in the parametric model case. The effect of smearing on prediction MSE is shown and so is its computation. A model-based bootstrap estimate of prediction MSE is proposed, which leads to competitive results, as shown via simulation. Australian farm survey data are used for illustration. (16 refs.)
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