Open Access
February 2012 Local proper scoring rules of order two
Werner Ehm, Tilmann Gneiting
Ann. Statist. 40(1): 609-637 (February 2012). DOI: 10.1214/12-AOS973


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.


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Werner Ehm. Tilmann Gneiting. "Local proper scoring rules of order two." Ann. Statist. 40 (1) 609 - 637, February 2012.


Published: February 2012
First available in Project Euclid: 7 May 2012

zbMATH: 1246.86013
MathSciNet: MR3014319
Digital Object Identifier: 10.1214/12-AOS973

Primary: 62C99
Secondary: 62M20 , 86A10

Keywords: density forecast , Euler equation , Hyvärinen score , proper scoring rule , tangent construction

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • February 2012
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