%0 Journal Article
%T Estimation of Extreme Values by the Average Conditional Exceedance Rate Method
%A A. Naess
%A O. Gaidai
%A O. Karpa
%J Journal of Probability and Statistics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/797014
%X This paper details a method for extreme value prediction on the basis of a sampled time series. The method is specifically designed to account for statistical dependence between the sampled data points in a precise manner. In fact, if properly used, the new method will provide statistical estimates of the exact extreme value distribution provided by the data in most cases of practical interest. It avoids the problem of having to decluster the data to ensure independence, which is a requisite component in the application of, for example, the standard peaks-over-threshold method. The proposed method also targets the use of subasymptotic data to improve prediction accuracy. The method will be demonstrated by application to both synthetic and real data. From a practical point of view, it seems to perform better than the POT and block extremes methods, and, with an appropriate modification, it is directly applicable to nonstationary time series. 1. Introduction Extreme value statistics, even in applications, are 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 generalized (asymptotic) extreme value distribution with unknown parameters to be estimated on the basis of the observed data [1, 2]. Or it is assumed that the exceedances above high thresholds follow a generalized (asymptotic) Pareto distribution with parameters that are estimated from the data [1¨C4]. 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 the statistical tests to decide this issue are rarely precise enough to completely 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. On the other hand, one can reasonably assume that in most cases long time series obtained from practical measurements do contain values that are large enough to provide useful information about extreme events that are truly asymptotic. This cannot be strictly proved in general, of course, but the accumulated experience indicates that asymptotic extreme value distributions do provide reasonable, if not always very accurate, predictions when based on measured data. This is amply documented in the vast literature on the subject, and good references to this literature are [2, 5, 6]. In an effort to
%U http://www.hindawi.com/journals/jps/2013/797014/