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

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  • Sasaki, Yuya
  • Wang, Yulong

Abstract

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.

Suggested Citation

  • Sasaki, Yuya & Wang, Yulong, 2024. "On uniform confidence intervals for the tail index and the extreme quantile," Journal of Econometrics, Elsevier, vol. 244(1).
    • Handle: RePEc:eee:econom:v:244:y:2024:i:1:s0304407624002100
    DOI: 10.1016/j.jeconom.2024.105865
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    References listed on IDEAS

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