Journal of Official Statistics, Vol.15, No.4, 1999. pp. 537–550

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A Conditional Analysis of Some Small Area Estimators in Two Stage Sampling


The conditional approach in sampling on finite populations analyses the performance of the’estimators for the conditional sample space Uc containing samples having some specific properties. The use of conditional arguments in sampling for small area estimation has been studied for the case of simple random sampling. In this article we treat a more realistic situation. We refer to a two-stage sampling design with stratification of the primary sampling units. In each stratum a single primary sampling unit is selected with probability proportional to’size. The secondary sampling units are selected without replacement and with equal probabilities. This design is generally used in household surveys conducted by the National Statistics Institute of Italy. We consider the following estimators: expansion, ratio, synthetic, and composite expressed as a linear combination of the ratio and synthetic estimators.

The conditional analysis is developed for the reference set Uc that contains all possible samples’that have a fixed number of primary sampling units belonging to the small area. We then develop the expressions of the variance and the bias of the four estimators. An empirical analysis concludes the work.

Conditional bias; conditional variance; conditional mean squared

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