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Biometrika 2005 92(1):213-227; doi:10.1093/biomet/92.1.213
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© 2005 Biometrika Trust

Exploiting occurrence times in likelihood inference for componentwise maxima

Alec Stephenson1 and Jonathan Tawn2

1 Department of Statistics, Division of Economic and Financial Studies, Macquarie University, NSW 2109, Australia alec.stephenson{at}mq.edu.au, 2 Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, U.K. j.tawn{at}lancaster.ac.uk

Multivariate extreme value distributions arise as the limiting distributions of normalised componentwise maxima. They are often used to model multivariate data that can be regarded as the componentwise maxima of some unobserved underlying multivariate process. In many applications we have extra information. We often know the locations of the maxima within the underlying process. If the process is temporal this knowledge is frequently available through the dates on which the maxima are recorded. We show how to incorporate this extra information into maximum likelihood procedures. Asymptotic and small-sample efficiency results are presented for the dependence parameter in the logistic parametric sub-class of bivariate extreme value distributions. We conclude with an application to sea levels.

Key Words: Asymptotic efficiency; Maximum likelihood; Multivariate extreme value distribution; Sea level

Received April 2003. Revised August 2004.


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