On Uniform Confidence Intervals for the Tail Index and the Extreme Quantile

Yuya Sasaki, Yulong Wang

Journal of Econometrics, September 2024

Yulong Wang

Economics Department

Center for Policy Research

Research Methods

Journal of Econometrics

Yulong Wang

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.