Is the mode elicitable relative to unimodal distributions?
成果类型：
Article
署名作者：
Heinrich-Mertsching, Claudio; Fissler, Tobias
署名单位：
Vienna University of Economics & Business
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asab065
发表日期：
2022
页码：
11571164
关键词：
摘要：
A statistical functional is said to be 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 that the mode is not elicitable if the true distribution can follow any Lebesgue density. We strengthen the result of substantially, showing that the mode is not elicitable 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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