Proper local scoring rules

TY - JOUR

T1 - Proper local scoring rules

AU - Parry, Matthew

AU - Dawid, A. Philip

AU - Lauritzen, Steffen L.

PY - 2012/2

Y1 - 2012/2

N2 - 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.

AB - 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.

U2 - 10.1214/12-AOS971

DO - 10.1214/12-AOS971

M3 - Journal article

SN - 0090-5364

VL - 40

SP - 561

EP - 592

JO - Annals of Statistics

JF - Annals of Statistics

IS - 1

ER -