Elicitation and identification of properties,

I. Steinwart, C. Pasin, R. Williamson, and S. Zhang

Abstract:

Properties of distributions are real-valued functionals such as the mean, quantile or conditional
value at risk. A property is elicitable if there exists a scoring function such that minimization of the
associated risks recovers the property. We extend existing results to characterize the elicitability of
properties in a general setting. We further relate elicitability to identifiability (a notion introduced
by Osband) and provide a general formula describing all scoring functions for an elicitable property.
Finally, we draw some connections to the theory of coherent risk measures