Journal article
Proper local scoring rules
- Abstract:
- We investigate proper scoring rules for continuous distributions on the real line. It is known that the log score is the only such rule that depends on the quoted density only through its value at the outcome that materializes. Here we allow further dependence on a finite number $m$ of derivatives of the density at the outcome, and describe a large class of such $m$-local proper scoring rules: these exist for all even $m$ but no odd $m$. We further show that for $m\geq2$ all such $m$-local rules can be computed without knowledge of the normalizing constant of the distribution.
- Publication status:
- Published
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- Publisher copy:
- 10.1214/12-AOS971
Authors
- Journal:
- Annals of Statistics More from this journal
- Volume:
- 40
- Issue:
- 1
- Pages:
- 561-592
- Publication date:
- 2011-01-26
- DOI:
- ISSN:
-
0090-5364
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:184649
- UUID:
-
uuid:80e9c2eb-c802-4240-841b-1e8cde1b5e41
- Local pid:
-
pubs:184649
- Source identifiers:
-
184649
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright date:
- 2011
- Notes:
-
Published in at http://dx.doi.org/10.1214/12-AOS971 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org)
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