I am trying to understand linear and GREG survey sample weighting adjustments through some examples. Page 85 of this paper by Calton and Flores-Cervantes shows the adjusted weights using the different weighting methods. The algorithms for Cell weighting and Raking are shown but not for the other methods. Can anybody show me how it was done for linear weighting adjustment and give me some clue on how to proceed about the other methods? I would prefer a step-by-step calculation but I appreciate too how this can be done through R.
It seems the link can't load the PDF directly so I linked to the abstract page instead. The full text can be downloaded from the sidebar link.
Below is a screenshot of Table 1 in page 84 that shows the initially weighted sample and population joint distributions for two auxiliary variables.
Below is a screenshot of Table 2 that shows the weighting adjustments from the different methods.