Variance estimation in two-step calibration for nonresponse adjustment

Rota and Laitila (2015) suggest an alternative two-step calibration estimation resulting from combining two calibration estimation approaches, i.e., linear calibration (Särndal and Lundström, 2005) and propensity score calibration (Chang and Kott, 2008), when the functional form of the response probability is assumed to be known. The first step focuses on estimating this function and the second step on estimating the total of a survey variable. This paper extends these previous findings by deriving an approximate variance expression and suggesting a variance estimator for the two-step estimator. The paper also justifies the use of sample-level auxiliary information in the first step of estimation, deferring the use of population-level auxiliary information to the second step of estimation