On uniform confidence intervals for the tail index and the extreme quantile

This paper presents two results concerning uniform confidence intervals for the tail index and the extreme quantile. First, we show that there exists a lower bound of the length for confidence intervals that satisfy the correct uniform coverage over a nonparametric family of tail distributions. Seco...

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Bibliographic Details
Published inJournal of econometrics Vol. 244; no. 1; p. 105865
Main Authors Sasaki, Yuya, Wang, Yulong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2024
Subjects
Extreme quantile
Honest confidence interval
Impossibility
Tail index
Uniform inference
Impossibility
Honest confidence interval
Extreme quantile
Tail index
Uniform inference
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Summary:This paper presents two results concerning uniform confidence intervals for the tail index and the extreme quantile. First, we show that there exists a lower bound of the length for confidence intervals that satisfy the correct uniform coverage over a nonparametric family of tail distributions. Second, in light of the impossibility result, we construct honest confidence intervals that are uniformly valid by incorporating the worst-case bias in the nonparametric family. The proposed method is applied to simulated data and real data of financial time series.
ISSN:0304-4076
DOI:10.1016/j.jeconom.2024.105865