Local proper scoring rules of order two

Abstract

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if it encourages truthful reporting. It is local of order $k$ if the score depends on the predictive density only through its value and the values of its derivatives of order up to $k$ at the realizing event. Complementing fundamental recent work by Parry, Dawid and Lauritzen, we characterize the local proper scoring rules of order 2 relative to a broad class of Lebesgue densities on the real line, using a different approach. In a data example, we use local and nonlocal proper scoring rules to assess statistically postprocessed ensemble weather forecasts.

Published in at http://dx.doi.org/10.1214/12-AOS973 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Proper local scoring rules
• Proper local scoring rules on discrete sample spaces
• Local proper scoring rules of order two

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