Open Access
February 2012 Proper local scoring rules
Matthew Parry, A. Philip Dawid, Steffen Lauritzen
Ann. Statist. 40(1): 561-592 (February 2012). DOI: 10.1214/12-AOS971


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 ≥ 2 all such m-local rules can be computed without knowledge of the normalizing constant of the distribution.


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Matthew Parry. A. Philip Dawid. Steffen Lauritzen. "Proper local scoring rules." Ann. Statist. 40 (1) 561 - 592, February 2012.


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

zbMATH: 1246.62011
MathSciNet: MR3014317
Digital Object Identifier: 10.1214/12-AOS971

Primary: 62C99
Secondary: 62A99

Keywords: Bregman score , concavity , divergence , Entropy , Euler–Lagrange equation , homogeneity , integration by parts , local function , score matching , variational methods

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • February 2012
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