Quotation Heinrich-Mertsching, Claudio, Fissler, Tobias. 2021. Is the mode elicitable relative to unimodal distributions? Biometrika.


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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 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.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Biometrika
Citation Index SCI
WU Journalrating 2009 A
WU-Journal-Rating new FIN-A, VW-B, WH-A
Language English
Title Is the mode elicitable relative to unimodal distributions?
Year 2021
Reviewed? Y
URL https://doi.org/10.1093/biomet/asab065
DOI https://doi.org/10.1093/biomet/asab065
Open Access Y
Open Access Link https://doi.org/10.1093/biomet/asab065
JEL MSC classes: 62C99, 62F07, 62F10

Associations

People
Fissler, Tobias (Details)
External
Heinrich-Mertsching, Claudio (Norwegian Computing Center Oslo, Norway)
Organization
Institute for Statistics and Mathematics IN (Details)
Research areas (Ă–STAT Classification 'Statistik Austria')
1113 Mathematical statistics (Details)
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