Multiple and ridge model calibration for sample surveys

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. However, model calibration provides a different set of weights for each variable of interest. To overcome this problem calibration can be 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 provided with respect to the sampling design. The issue of an eventual high variability of the weights is addressed by using ridge calibration and relaxing binding constraints on the variables included for efficiency purposes in the set of calibration equations. A simulation study is also presented to etter understand the finite size sample behavior of the estimators discussed in the paper.