Calibration weighting was introduced as a tool for reducing the standard errors of many, if not most, finite-population estimates produced from a survey sample by mildly adjusting the sample's inverse-probability weights. Calibration weighting does this by forcing the weighted sums of certain ‘calibration’ variables to equal their known (or better-estimated) population totals. In the absence of unit (element-level) nonresponse, the weight-adjustment function produces an adjustment factor for each inverse-probability weight that tends to unity in large samples. When there is unit nonresponse in a survey, however, the weight-adjustment factor in calibration weighting need no longer be near unity. Instead, it can implicitly estimate the inverse of each unit's probability of response under an assumed response model. As a result, calibration weighting can remove, or at least greatly reduce, the potential for nonresponse bias in the resulting estimates. Moreover, if the survey variable of interest is assumed to be random variable with an expectation linear in the calibration variables and unaffected by whether or not the unit responds when selected, then calibration weighting produces an unbiased estimator for the survey-variable's population total whether or not the selection model implied by the weight-adjustment function holds. When the response model contains variables with values known only for respondents, the situation is a bit more complicated.
Calibration weighting in survey sampling
Kott, P. (2015). Calibration weighting in survey sampling. Wiley Interdisciplinary Reviews: Computational Statistics, 8(1), 39-53. https://doi.org/10.1002/wics.1374