I have a response dataset that is very far from representative. The sample was drawn SRS. Some population groups are much more likely to respond than others, so calibration (to known population totals) have been used in estimation.
Some of the correction factors are quite extreme (very far form 1). I am unsure as to how that affects the standard error (or variance) of the estimators. Will large correction factors make standard errors larger, smaller or have no effect at all?
Is there a known connection between the standard error of calibration estimators and the correction factors, i.e. a formula? Or even an asymptotic relationship?