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An efficient semiparametric maxima estimator of the extremal index

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Abstract

The extremal index θ, a measure of the degree of local dependence in the extremes of a stationary process, plays an important role in extreme value analyses. We estimate θ semiparametrically, using the relationship between the distribution of block maxima and the marginal distribution of a process to define a semiparametric model. We show that these semiparametric estimators are simpler and substantially more efficient than their parametric counterparts. We seek to improve efficiency further using maxima over sliding blocks. A simulation study shows that the semiparametric estimators are competitive with the leading estimators. An application to sea-surge heights combines inferences about θ with a standard extreme value analysis of block maxima to estimate marginal quantiles.

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  1. Department of Statistical Science, University College London, Gower Street, London, WC1E 6BT, UK

    Paul J. Northrop

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  1. Paul J. Northrop
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Correspondence to Paul J. Northrop.

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Northrop, P.J. An efficient semiparametric maxima estimator of the extremal index. Extremes 18, 585–603 (2015). https://doi.org/10.1007/s10687-015-0221-5

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  • DOI: https://doi.org/10.1007/s10687-015-0221-5

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