Prediction of finite population totals based on the sample distribution

Abstract

In this article we study the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors condition on the sample values of the target outcome variable, the sampling weights of the sample units and possibly on known population values of auxiliary variables.

The prediction problem is solved by estimating the expectation of the outcome values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction variance is estimated by a combination of an inverse sampling procedure and the bootstrap method. An important outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.

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