The NAS Panel notes the following about several statistics used in proxy studies:
If are the predictions from a linear regression of on the proxies, and the period of interest is the calibration period, then RE, CE, and are all equal.
Here’s a result about MBH methods (and applicable to related methods with re-scaling) that has not been reported:
If are the predictions from an estimate of in which has been re-scaled so that its standard deviation matches the standard deviation of the target, and the period of interest is the calibration period, then
(1) CE=RE = 2*r-1.
I can prove this (the proof is fairly trivial but you have to think a little or else some one else would have observed it already) and have verified it against actual results. Notice that the relation is with directly and not . I thought of this when I saw a comment of Bürger and Cubasch about correlations, in which they mentioned that correlation and r2 were inappropriate when scale was involved. It’s not like I’m some advocate of one statistic over another, so much as someone who says that you should look at all aspects. In this case, there’s a reason why correlation links directly to explained variance. OK, Gerd, do you agree? This would be a good puzzle for Rob Wilson (who uses re-scaling procedures) to think about as well.