Abstract
A scoring function is consistent for the $\alpha$-quantile functional if, and only if, it is generalized piecewise linear (GPL) of order $\alpha$, up to equivalence. Expressed differently, loss functions that yield quantiles as Bayes rules are GPL functions. We review and discuss this basic decision-theoretic result with focus on Thomson’s pioneering characterization.
Information
Published: 1 January 2013
First available in Project Euclid: 8 March 2013
zbMATH: 1327.62035
MathSciNet: MR3202632
Digital Object Identifier: 10.1214/12-IMSCOLL912
Subjects:
Primary:
62C05
Secondary:
91B06
Keywords:
Bayes rule
,
consistent scoring function
,
fractile
,
optimal point forecast
,
proper scoring rule
,
quantile
Rights: Copyright © 2010, Institute of Mathematical Statistics
