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Office of Survey Methods Research
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Published Year: 2003
Survey/Program(s): General Methodology
Catalog: Statistical Survey Paper
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On Small Area Estimation under Informative Sampling
Abstract
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.