Notes on the variance of a pseudo-weighted estimator for selection bias correction

This paper proposes analytical variance estimation formulas for the estimated population mean from an extended pseudo weighting method developed by [1] (LSdW). LSdW is meant to correct selection bias in a nonprobability sample, also when the nonprobability sample or the reference probability sample has a large inclusion fraction. Since samples with large inclusion fractions often require massive computation resources, having an analytical expression for the variance will be more time-efficient compared to resampling methods. In addition, we show that LSdW is a consistent estimator of the population mean under certain assumptions. To deal with different designs of the probability sample, probability proportional to size (PPS) sampling and simple random sampling (SRS) are considered, and the variance estimator formulas are given accordingly. The proposed formulas are evaluated by a simulation study and it shows that the proposed formulas give reasonable estimates in terms of relative bias and coverage of the confidence interval.