Local Proper Scoring Rules of Order Two

Details Local Proper Scoring Rules of Order Two Local Proper Scoring Rules of Order Two

2011-02-24

arxiv.org/abs/1102.5031v1

Mathematics

Statistics Theory

Scientific paper

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 (2011), we characterize the local proper scoring rules of order two relative to a broad class of Lebesgue densities on the real line, using a different approach. In a data example, we use local and non-local proper scoring rules to assess statistically postprocessed ensemble weather forecasts.

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