The Annals of Statistics

Proper local scoring rules

Matthew Parry, A. Philip Dawid, and Steffen Lauritzen

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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.

Article information

Ann. Statist., Volume 40, Number 1 (2012), 561-592.

First available in Project Euclid: 7 May 2012

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Zentralblatt MATH identifier

Primary: 62C99: None of the above, but in this section
Secondary: 62A99: None of the above, but in this section

Bregman score concavity divergence entropy Euler–Lagrange equation homogeneity integration by parts local function score matching variational methods


Parry, Matthew; Dawid, A. Philip; Lauritzen, Steffen. Proper local scoring rules. Ann. Statist. 40 (2012), no. 1, 561--592. doi:10.1214/12-AOS971.

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