The ACER Method

Extreme value statistics, even in applications, is generally based on asymptotic results. This is done either by assuming that the epochal extremes, for example, yearly extreme wind speeds at a given location, are distributed according to the so-called generalized (asymptotic) extreme value distribution with unknown parameters to be estimated on the basis of the observed data, cf. Chap. 2 or Coles (An introduction to statistical modeling of extreme values. Springer series in statistics. Springer, London, 2001) and Beirlant et al. (Statistics of extremes. Wiley, Chichester, 2004), or by assuming that the exceedances above high thresholds follow a generalized (asymptotic) Pareto distribution with parameters that are estimated from the data, cf. Chap. 3 or Coles (An introduction to statistical modeling of extreme values. Springer series in statistics. Springer, London, 2001), Beirlant et al. (Statistics of extremes. Wiley, Chichester, 2004), Davison and Smith (J R Stat Soc B 52(3):393–442, 1990), and Reiss and Thomas (Statistical analysis of extreme values, 3rd edn. Birkhäuser, Basel, 2007). As was discussed in Chap. 1, the major problem with both of these approaches is that the asymptotic extreme value theory itself cannot be used in practice to decide to what extent it is applicable for the observed data. And since statistical tests to decide this issue are rarely precise enough to settle this problem, the assumption that a specific asymptotic extreme value distribution is the appropriate distribution for the observed data is based more or less on faith or convenience. However, even if the situation might be tolerable, it is clearly not satisfactory. In an effort to improve on the described state of affairs, an approach to the extreme value prediction problem has been developed that is less restrictive and more flexible than the ones using only asymptotic theory (Naess and Gaidai (2009) Struct Saf 31:325–334; Naess et al. (2013) J Probab Stat. https://doi.org/10.1155/2013/797014 ). The approach is based on two separate components that are designed to improve on two important aspects of extreme value prediction based on observed data.