Matching Information from Two Independent Informative Samples

Statistical matching deals with the problem of how to combine information collected in different samples taken from the same target population, but on partly different survey variables. The purpose of this paper is to analyze the statistical matching problem under informative sampling designs, when applying the sample likelihood approach. First, a conditional independence assumption is made, which allows to define an identifiable population model under which the conditions guaranteeing the identifiability and estimability of the sample likelihood are investigated. Next, the uncertainty in statistical matching under informative sampling designs is discussed, with particular attention to the three-variate normal case. A simulation experiment illustrating the theoretical results is performed.