  Survey statisticians make use of the available auxiliary information to
improve estimates. One important example is given by calibration estimation,
that seeks for new weights that are close (in some sense) to the basic design
weights and that, at the same time, match benchmark constraints on available
auxiliary information. Recently, multiple frame surveys have gained much
attention and became largely used by statistical agencies and private
organizations to decrease sampling costs or to reduce frame undercoverage
errors that could occur with the use of only a single sampling frame. Much
attention has been devoted to the introduction of different ways of combining
estimates coming from the different frames. We will extend the calibration
paradigm, developed so far for one frame surveys, to the estimation of the
total of a variable of interest in dual frame surveys as a general tool to
include auxiliary information, also available at different levels. In fact,
calibration allows us to handle different types of auxiliary information and
can be shown to encompass as a special cases some of the methods already
proposed in the literature. The theoretical properties of the proposed class of
estimators are derived and discussed, a set of simulation studies is conducted
to compare the efficiency of the procedure in presence of different sets of
auxiliary variables. Finally, the proposed methodology is applied to data from
the Barometer of Culture of Andalusia survey.
