Calibration inspired by Semiparametric Regression as aTreatment for Nonresponse

In the last decade, calibration has been used to reduce both sampling error and nonresponse bias in surveys. In the presence of auxiliary variables with known population totals or with known values on the originally sampled units, the calibration procedure generates final weights for observations that, when applied to those auxiliary variables, yield their population totals or unbiased estimates of these totals, respectively. A single set of variables and a single calibration step is employed to this end. In this article, we extend this approach to allow for more flexible implicit description of the relationship of the auxiliary variables with either the response probabilities or the survey variable(s). By using penalized splines the simplicity of the original proposal and the linearity of the estimator are preserved. The conditions under which the proposed estimator of the total is design consistent and its asymptotic properties are explored, and its finite sample behavior is investigated via simulations.