Abstract
In this paper we investigate the prediction of the population total T = Σ N k=1 Y k under regression superpopulation models when the explanatory variable vector x is measured with error. Predictors T ̂ of the population total T which are functions of estimators \\ ̂ gb of the regression coefficient parameter β are investigated. In particular, by considering the ordinary least-squares estimator of β, we have the best unbiased predictor (BLU — Royall, 1976, Bolfarine and Zacks, 1992) of T, denoted by T ̂ BLU . Exploring the asymptotic normality of \\ ̂ gb under a set of assumptions, we study the asymptotic behavior of the predictor T ̂ , establishing its asymptotic normality. In the case of unique and several explanatory variables, comparisons are made in terms of the predictive variances of the asymptotic distributions. Surprisingly, the main conclusion is that T ̂ BLU is the predictor that behaves asymptotically best.
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