Estimating POT second-order parameter for bias correction

Abstract

The stable tail dependence function provides a full characterisation of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the Peaks-Over-Threshold (POT) second-order parameter. For this second-order parameter, this paper introduces a penalised estimator that discourages it from being too close to zero. This paper then establishes this estimator's asymptotic consistency, uses it to correct the bias in the estimation of the stable tail dependence function, demonstrates its desirable empirical properties in the estimation of the extremal dependence structures, and illustrates it with an application to liability claim data.

Keywords:

• Extreme value theory
• peaks-over-threshold
• second-order parameter
• bias correction

Mathematical Subject classification:

• 62H12

Acknowledgments

We thank the authors of Beirlant et al. (2016) for sending their codes, Axel Bücher and Stanislav Volgushev for the fruitful discussion, and anonymous referees for insightful and helpful feedback.

Disclosure statement

No potential conflict of interest was reported by the author(s).