Is the mode elicitable relative to unimodal distributions?

Claudio Heinrich-Mertsching; Tobias Fissler

doi:10.1093/biomet/asab065

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arXiv · 2109.00464

Is the mode elicitable relative to unimodal distributions?

Claudio Heinrich-Mertsching·Tobias Fissler

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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.

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Claudio Heinrich-Mertsching, Tobias Fissler. 2021-09-01. Is the mode elicitable relative to unimodal distributions?. https://doi.org/10.1093/biomet%2Fasab065

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