1. Introduction
Guillaume Chauvet and Guylène Tandeau de Marsac
When studying a finite population, sometimes no sampling frame covers that population completely, and it is necessary to select samples from two or more sampling frames in order to represent all individuals. Many methods of estimation on multiple sampling frames have been proposed to pool these samples (Hartley 1962; Bankier 1986; Kalton and Anderson 1986; Mecatti 2007; Rao and Wu 2010); see also the review articles by Lohr (2009, 2011) and the referenced articles for a complete picture. Note that the Mecatti method (2007) is inspired by the work of Lavallée (2002, 2007) on the Generalized Weight Share Method. In Section 2, we present different estimation methods for multiple sampling frames.
In Section 3, we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. This framework corresponds to INSEE expansion surveys: an initial sample of dwellings is selected from the communes of the master sample (Bourdalle, Christine and Wilms 2000), and a second sample is selected and surveyed from the communes of the same master sample to target a specific subpopulation. We have two survey measurements from two independent samples at the second stage of the design. We apply estimation methods to multiple sampling frames to pool these two samples. We show that the estimators examined can in this case be calculated conditional on the first stage of selection, which simplifies calculation particularly for Hartley’s optimal estimator (1962). In Section 4, we compare the performance of these estimators as part of a simulation study. We present our conclusion in Section 5.
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