M ii

Classical small area estimation techniques assume either that all the areas are represented in the sample or that the selection of the areas to the sample is noninformative. When the areas are sampled with unequal selection probabilities that are related to the values of the response variable, the classical estimators are biased; the magnitude of the bias depends on the sampling fraction and the covariance between the sampling weights and the response variable. We illustrate this point using very simple models employing the notions of the sample distribution and sample-complement distribution. We suggest simple unbiased estimators based on these distributions. Key words: Sample distribution, Sample-complement distribution 1. The sample and sample-complement distributions Consider a finite population U consisting of N units belonging to M areas, with iN units in area i