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Oct 19, 2020 at 15:38 comment added usul @aduh, Hmm, I don't know. It must have to do with $F$ being required to be weakly increasing, implying somehow that it's not possible to modify $F$ on a set of measure zero.
Oct 19, 2020 at 0:09 comment added aduh Is there an easy way to see that CRPS is indeed strictly proper on probabilities over $[0,1]$? I'm having trouble showing it.
Oct 18, 2020 at 14:00 history edited usul CC BY-SA 4.0
correction
Oct 18, 2020 at 13:59 comment added usul @aduh ah, thanks for catching that! I assume it's because the expected score becomes $-\infty$ for many (any?) forecasts, making it weakly proper as they say.... But at least on $[0,1]$ it will be unrestricted.
Oct 18, 2020 at 6:37 comment added aduh It looks like they say it's strictly proper only for the subclass of $\mathcal P$ consisting of those probability measures with finite first moment.
Oct 18, 2020 at 3:36 history answered usul CC BY-SA 4.0