Efficient bootstrap estimates for tail statistics

Abstract

Abstract. Bootstrap resamples can be used to investigate the tail of empirical distributions as well as return value estimates from the extremal behaviour of the sample. Specifically, the confidence intervals on return value estimates or bounds on in-sample tail statistics can be obtained using bootstrap techniques. However, non-parametric bootstrapping from the entire sample is expensive. It is shown here that it suffices to bootstrap from a small subset consisting of the highest entries in the sequence to make estimates that are essentially identical to bootstraps from the entire sample. Similarly, bootstrap estimates of confidence intervals of threshold return estimates are found to be well approximated by using a subset consisting of the highest entries. This has practical consequences in fields such as meteorology, oceanography and hydrology where return values are calculated from very large gridded model integrations spanning decades at high temporal resolution or from large ensembles of independent and identically distributed model fields. In such cases the computational savings are substantial.

Global Ocean Extreme Wave Heights from Spatial Ensemble Data

“…The difference between these values, CI 0.95 5 CL 0.975 2 CL 0.025 , is the 95% confidence interval; statistically, there is a 95% probability that the true value of the 100yr return period significant wave height lies within this interval around the estimate H 100 s (Muir and El-Shaarawi 1986;Mathiesen et al 1994). A primary concern in the estimation of extreme values is reducing the CI and hence increasing the confidence in the extreme value estimate (Mathiesen et al 1994;Breivik et al 2013Breivik et al , 2014Breivik and Aarnes 2017;Meucci et al 2018). As a result, a number of recent studies have examined approaches to reduce the CI (Bulgakov et al 2018;Takbash et al 2019;Meucci et al 2018).…”

“…Present-day weather prediction systems include a stochastic element to account for the intrinsic uncertainty in initial conditions by running an ensemble of forecasts, each initiated with slightly perturbed initial conditions, rather than a single deterministic forecast (Lewis 2005). Breivik et al (2013Breivik et al ( , 2014 and Meucci et al (2018) have taken advantage of the fact that at long lead time (9-10 days) these forecasts diverge to the point where they have low correlation. In such circumstances, each forecast in the ensemble potentially becomes an independent realization of a potential sea state.…”

“…Following the general concept developed by Breivik et al (2013Breivik et al ( , 2014 and Meucci et al (2018), the present study explores whether a spatial ensemble of data can be used to reduce potential errors and the magnitude of confidence limits for estimates of H 100 s . Both the ERAI reanalysis model dataset and the altimeter dataset of Young et al (2017) and Ribal and Young (2019) are used and the EVA methods described by Takbash et al (2019) (i.e., PoT analysis).…”

“…Both the ERAI reanalysis model dataset and the altimeter dataset of Young et al (2017) and Ribal and Young (2019) are used and the EVA methods described by Takbash et al (2019) (i.e., PoT analysis). Rather than pooling independent model forecasts (Breivik et al 2013(Breivik et al , 2014Meucci et al 2018), we explore whether data from a number of independent spatial domains can be combined (pooled) to create a synthetic dataset with an equivalent duration that is the sum of the durations of the separate areas pooled.…”

“…To be able to pool data from spatial regions they must be independent and identically distributed (Goda 1988;Coles 2001;Breivik et al 2013;Breivik et al 2014). In the present context, these requirements become the following:…”