Getting back to CISS for a bit. The selection process for the next block to sample was basically to look at the variability of the strata estimators and pick a stratum in proportion to it's "uncertainty" (technically, the quantity I use is the variance of the unsampled data, not the sampled data, so I call it uncertainty rather than variance). I did this without a bunch of mathematical justification because it seemed intuitive enough. Of course, that attitude can get one in a lot of trouble so I'm happy to have found a reference that has already done most of the heavy lifting.
Reference: Shahbaz, MQ., Shabaz, S., and Hanif, M. International Journal for Open Problems in Computational Mathematics, Vol 4, No 1, March 2011.
It starts with the Horvitz and Thompson Estimator (another paper I should include) and looks particularly at the 2-valued sample. This isn't super interesting in and of itself, but the introduction is good annotated bibliography starting with Hansen's paper that I reviewed last spring. I could have gotten most of it by simply doing a forward reference on Hansen, but now that's one less thing.
The main takeaway is the variance computation. As I said, my uncertainty isn't really a variance, but if the CISS technique was used to create a sample that would then be used for leveraged analysis, I'd need to flip that around and be able to estimate the sample variance. So, it could come in handy.
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