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Abstract:
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Ratio estimation is often useful for Official Statistics regarding energy, and for agriculture, econometrics, and perhaps many other applications in business, social science, and other areas. Notably, ratio estimation is very often useful for highly skewed establishment survey populations where, per Brewer(2002), mid-page 111, there should be at least as much implicit heteroscedasticity as for that of the classical ratio estimator (CRE). The concepts of design-based and model-based ratio estimation and sampling are reviewed and compared. Meaningfulness might be enhanced by understanding this comparison. Note that here the design-based case is actually model-assisted, but is being contrasted with the strictly model-based methodology, where probability of selection does not enter into the estimation, actually 'prediction,' of totals, and may or may not be used for sample selection. These model-based and design-based interpretations of the CRE, their corresponding concepts of variance and bias, with relation to sampling and estimation, are reviewed, and extensions of these estimators are also considered. Simple random sampling, cutoff, and unequal probability of selection methodologies are of interest. Stratification is often highly useful with either approach. Even if a regression model is not explicitly considered, this review considers the role it still plays. The relationship of heteroscedasticity, explicitly addressed in model-based estimation, to cluster sampling for unequal-sized censused clusters, is a point of interest: Each observation in a model-based sample may be treated as a cluster unit for which we have a census. (Again, see Brewer(2002), mid-page 111.)
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