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Context, Goal: To estimate the quantitative effect of the treatment on a continuous dependent variable, while controlling for another continuous variable.

I have one sample each from a test (n=918) and control (n=2,048) group. There is another variable, let's call it weight. The distribution of weight is arbitrary and very different among test and control groups (long-tailed, actually).

I need to estimate the difference in means between the test and control groups, while controlling for weight.

This is what I've come up with:

  1. Obtain kernel density estimate (KDE) to approximate the distribution of weight in the test group.
  2. Use rejection sampling on the control group to generate sample sets. Each sample set would therefore have the same distribution of weight as in the test group.
  3. Generating large number of such sample sets would provide confidence limits, apart from expected value of the distributed variable - kind of like a bootstrap.

Questions

  1. Is this a valid approach? The only other place I've seen a similar idea is this question.
  2. Is there a better alternative? Better could be simpler, more practical, more rigorous, etc.
  3. Would this method work if the sample size of the control group were much less relative to the test group?
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