Calibrazione multipla rispetto al modello nell'inferenza su popolazioni finite

Model calibration has been shown to provide more efficient estimates than classical calibration when the values of one or more auxiliary variables are available for each unit in the population and the relationship between such variables and the variable of interest is more complex than a linear one. Model calibration, though, provides a different set of weights for each variable of interest. To overcome this problem an estimator is proposed: calibration is pursued with respect to both the auxiliary variables values and the fitted values of the variables of interest obtained with parametric and/or nonparametric models. This allows for coherence among estimates and more efficiency if the model is well specified. The asymptotic properties of the resulting estimator are studied with respect to the sampling design. The issue of high variability of the weights is addressed by relaxing binding constraints on the variables included for efficiency purposes in the calibration equations. A simulation study is also presented to better understand the finite size sample behavior of the proposed estimator.