ExtremeCI: Realistic Confidence Intervals for Non-Stationary Extreme Value Statistics

This framework provides versatile algorithms to efficiently infer confidence intervals for extreme value statistics, such as extreme quantiles and return levels, that are representative of the asymmetric uncertainty spread, using extreme value theory extrapolation and the profile likelihood (see e.g., Coles (2001)). Unlike existing algorithms, the CI endpoints are found without the need for a strict prespecified range, can be covariate-dependent, and can use sample weights. This package is motivated by Zeder et al. (2023).

Confidence intervals based on the profile-likelihood method capture the uncertainty spread of extreme value statistics more realistically than most alternative methods (e.g. based on bootstraping of the delta-method), especially for return levels (high quantiles) and for the shape parameter, whose uncertainties are typically highly asymmetric (see e.g., Coles (2001)). For return levels and extreme quantiles, the profile likelihood method requires reparametrization of the likelihood function. With nonstationary models, this reparametrization is nontrivial and requires repetition for each local interval, which was not possible with existing R implementations. Furthermore, existing implementations require prespecified ranges for the CI endpoints search, which is impractical when the uncertainty spread is large or covariate-dependent, or when used as step in a greater pipeline. This package relies on novel binary-search procedures to efficiently find the profile likelihood CI endpoints. Lastly, inference can optionally be performed using sample weights. In summary, the novelties of this package for realistic extreme value confidence intervals are:

• efficient profile-likelihood CI endpoint search procedures without prespecified ranges, for both the peaks-over threshold (GPD) and block maxima (GEV) approaches,
• covariate-dependent CIs for nonstationary extreme value models, including for extreme quantiles and return levels,
• the option to use sample weights in inference.

Links

source code: released soon on https://github.com/opasche/ExtremeCI