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Natalja Lepik 《Acta Appl Math》2007,97(1-3):41-52
It is well known that the generalized regression (GREG) estimator of the finite population total is asymptotically unbiased.
Consequently, bias is negligible when the sample size is large. But the magnitude of the bias is not known, if we are estimating
small areas or operating with small samples. Furthermore, beside the sample size, the bias depends on the auxiliary variables,
on their relation to the study variable and on the sampling design. In small samples it is important to know sources of the
bias and in some cases to use a bias-corrected regression estimator. The aim of the present paper is to derive approximate
bias expressions of the GREG estimator under different population models and different sampling designs to study the magnitude
of the bias.
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