1 min read

Sparse linear systems and calibration of weights

Diego Zardetto (Italian national stats agency) wants to be able to calibrate sampling weights to population totals for regions.  This leads to a very large number of calibration variables and solving large linear systems.

Using the Matrix package in R, we can compute sparse QR decompositions instead of the dense ones used in the survey package.  Alternatively, using block-diagonal sparse matrices from the bdsmatrix package we can represent the linear system as a set of separate systems for each region. 

Which approach works best is an empirical question, but both should be fairly easy to implement (when I get a spare day to do it). 

Update: I didn’t, but the people at the Australian Bureau of Statistics did