Dbradke wrote:Thank you both very much for your replies. I agree that it is not too difficult to approximate the variance for a ratio using the delta method, especially following the Powell (2007) paper (which was actually the main reference I was using – it’s a great source!). The issue is that I don’t think Ne and N are independent, so I think it may be misleading to use a covariance of zero. However, it seems like that might be the only option, aside from not reporting a variance at all. Thanks again!
cooch wrote:
So, your 'thought problem' would be, if you assume independence, what does that do to your estimate of the variance? [Not hard with a bit of thought...]
Larkin's paper is indeed very good -- a very convenient tabulation of some common transformations, some interesting worked out applications, and a fair treatment of the underlying machinery [for the full treatment, Appendix 2 in the MARK book -- definitely less accessible than Larkin's paper, but partly because is has a different intent. Appendix 2 spends a lot of time trying to explain 'how it works', not just 'what to do'. Knowing how the Delta method -- or anything else -- works is important for those situations that arise when the Delta method doesn't work well.].
The other small comment about Larkin's paper is that there are a few nasty little typos in some of the equations which can cause problems (not at all Larkin's fault -- there are lot of clues in the paper that suggest said typos emerged when the editorial types -- who don't use LaTeX much, it would seem -- tried to typeset the equations...).
For example, eq. 2 in the paper is not correct -- the double-summation in the second term should be of , not (following Seber, 1982). In the incorrect version, is the variance, not the covariance. The equation requires to restrict it to covariances. And so on...
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