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Within the context of combining register and survey data, we consider here multisource estimation methods that make use of two or more proxy variables. Deficiency of coverage, relevance, and timeliness is often the reason that register-based estimation is not viable. When the lack of coverage can be limited to specific domains or variables, the problem can be remedied by the collection of supplementary survey data using the split-population or split-data approach. There would be only one value for each variable of interest now that the data supplement each other. Different multisource estimation approaches are needed for multiple proxy variables.

We shall classify the various scenarios using two conditions summarized in Table 1.1. (i) Whether one treats one of the proxy variables as the target measure and the others as associated with relevance bias – to be referred to as the asymmetric setting; the setting is symmetric otherwise, where either none of the proxy variables is considered to be the ideal measure, or all are correct measures which nevertheless do not have perfect population coverage, (ii) Whether it is necessary to have linked data at the individual or cell level – to be referred to as the linked setting; the setting is unlinked otherwise. Each of the approaches listed in Table 1.1 covers a variety of methods with an extensive body of literature. The following elaboration aims merely to provide a brief accessible overview, and the references given serve only as points of departure for further exploration.

Table 1.1 Indirect estimation using register and survey proxy variables.

Linked data	One target measure and relevance bias in the others?
	Yes (asymmetric)	No (symmetric)
Yes (linked)	Survey weighting Prediction modeling	Capture–recapture methods Structural equation modeling
No (unlinked)	Benchmark adjustment	Constrained optimization