On the Indirect Elicitability of the Mode and Modal Interval

TL;DR

This paper investigates whether the mode or modal interval can be indirectly elicited through scoring functions and concludes that neither can be, within the class of identifiable functionals, highlighting limitations in eliciting the mode.

Contribution

The paper proves that the mode and modal interval are not indirectly elicitable from any low-dimensional identifiable functional.

Findings

Mode is not elicitable using scoring functions.

Modal interval cannot be indirectly elicited.

Elicitation limitations for the mode are established.

Abstract

Scoring functions are commonly used to evaluate a point forecast of a particular statistical functional. This scoring function should be consistent, meaning the correct value of the functional is the Bayes act, in which case we say the scoring function elicits the functional. Recent results show that the mode functional is not elicitable. In this work, we ask whether it is at least possible to indirectly elicit the mode, wherein one elicits a low-dimensional functional from which the mode can be computed. We show that this cannot be done: neither the mode nor a modal interval are indirectly elicitable with respect to the class of identifiable functionals.