LOCAL PROPER SCORING RULES OF ORDER TWO

作者：Ehm Werner^*; Gneiting Tilmann

来源：Annals of Statistics, 2012, 40(1): 609-637.

DOI：10.1214/12-AOS973

• Density forecast
• Euler equation
• Hyvarinen score
• proper scoring rule
• tangent construction

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.

• 出版日期2012-2