A fundamental technique in survey sampling is to weight included units by the inverse of their probability of inclusion, which may be known (as in the case of sampling weights) or estimated (as in the case of nonresponse weights). The technique is closely associated with the design-based approach to survey inference, with the idea that units in the sample are representing a certain number of units in the population. I discuss weighting from a modeling perspective. Some common misconceptions of weighting will be addressed, including the idea that modelers can ignore the sampling weights, or that weighting necessarily reduces bias at the expense of increased variance, or that units entering the calculation of nonresponse weights should be weighted by their sampling weights. A robust model-based perspective suggests that selection weights cannot be ignored, but there may be better ways of incorporating them in the inference than via the standard Horvitz-Thompson estimator and its variants.
Statistical Methodology | Statistical Theory
Little, Rod, "WEIGHTING AND PREDICTION IN SAMPLE SURVEYS" (February 2009). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 81.