Variance estimation for ridge calibration estimation in survey sampling

Ridge calibration is a penalized calibration method in which the calibration constraint is replaced by a quadratic penalty term, thereby yielding soft calibration. In this study, we show that ridge calibration weights can be expressed in a general functional form. Building on this result, we establish the asymptotic properties of the ridge calibration estimator and propose an asymptotic variance estimator. We also consider penalty parameter selection methods designed to minimize the mean squared error of the resulting ridge calibration estimator, with additional adjustments applied to satisfy range restrictions when necessary. Through a limited set of simulation studies, we demonstrate that these selection methods reduce the mean squared error and that the proposed variance estimation method appropriately incorporates the applied penalty parameter.