Multiple frame sampling technique has been introduced by H.O. Hartley (1962, 1984), and further developments were due to J.N.K. Rao (1983) and J.N.K. Rao with S. Lohr (2006). A multiple frame sampling survey requires joint use of more than one sampling list (frame)and each one of them needs the most efficient estimate method. The frames, besides, may be overlapped, and so if we have k frames than there will be 2k – 1 disjointed domains (Mecatti, 2007). The type of data treated in multiple frame surveys is usually related to rare, elusive and, however, difficult-to-sample populations. In these situations it’s impossible to carry out a probabilistic sampling design and sampling data should be not so reliable, hence here a Bayesian estimate approach based on the joint use of sampling and extra-sampling information is proposed, specially referred to the case of two frames (dual frame). The aim of the proposed procedure, therefore, is to provide sampling estimates that, thanks to the increasing extra-sampling information relative effect, makes sampling results more stable and reliable.
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