Is the mode elicitable relative to unimodal distributions?

Claudio Heinrich-Mertsching, Tobias Fissler

Publication: Scientific journalJournal articlepeer-review

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 can be any strongly unimodal distribution with continuous Lebesgue density, i.e., a continuous density with only one local maximum. Likewise, the mode fails to be identifiable relative to this class.
Original languageEnglish
JournalBiometrika
DOIs
Publication statusPublished - 2021

Austrian Classification of Fields of Science and Technology (ÖFOS)

  • 101029 Mathematical statistics

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