Proper Local Scoring Rules

Details Proper Local Scoring Rules Proper Local Scoring Rules

2011-01-26

arxiv.org/abs/1101.5011v3

Mathematics

Statistics Theory

34 pages. Final version, accepted for publication in Annals of Statistics

Scientific paper

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 greater than or equal to 2 all such m-local rules can be computed without knowledge of the normalizing constant of the distribution.

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