Is the mode elicitable relative to unimodal distributions?
Statistics Theory
2023-05-10 v2 Methodology
Statistics Theory
Abstract
Statistical functionals are called elicitable if there exists a loss or scoring function under which the functional is the optimal point forecast in expectation. While the mean and quantiles are elicitable, it has been shown in Heinrich (2014) that the mode cannot be elicited if the true distribution can follow any Lebesgue density. We strengthen this result substantially, showing that the mode cannot be elicited if the true distribution is any distribution with continuous Lebesgue density and unique local maximum. Likewise, the mode fails to be identifiable relative to this class.
Keywords
Cite
@article{arxiv.2109.00464,
title = {Is the mode elicitable relative to unimodal distributions?},
author = {Claudio Heinrich-Mertsching and Tobias Fissler},
journal= {arXiv preprint arXiv:2109.00464},
year = {2023}
}
Comments
10 pages, 1 figure