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Journal of Probability and Statistics
Volume 2013, Article ID 797014, 15 pages
http://dx.doi.org/10.1155/2013/797014
Research Article

Estimation of Extreme Values by the Average Conditional Exceedance Rate Method

1Department of Mathematical Sciences and CeSOS, Norwegian University of Science and Technology, 7491 Trondheim, Norway
2Norwegian Marine Technology Research Institute, 7491 Trondheim, Norway
3Centre for Ships and Ocean Structures (CeSOS), Norwegian University of Science and Technology, 7491 Trondheim, Norway

Received 18 October 2012; Revised 22 December 2012; Accepted 9 January 2013

Academic Editor: A. Thavaneswaran

Copyright © 2013 A. Naess et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.