Simulation Study of the Calibration Technique in the Extremal Index Estimation

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Abstract

Classical extreme value methods were first derived when the underlying process is assumed to be a sequence of independent and identically distributed random variables. However, when observations are taken along the time and/or the space the independence is an unrealistic assumption. A relevant parameter that arises in this situation is the extremal index, θ, characterizing the degree of local dependence in the extremes of a stationary series. Most of the semi-parametric estimators of this parameter show a strong dependence on the threshold un, with an increasing bias and a decreasing variance as such a threshold decreases. A procedure based on the calibration methodology is here considered as a way of controlling the bias of an estimator. Point and interval estimates for the extremal index are obtained. A simulation study has been performed to illustrate the procedure.
Original languageUnknown
Title of host publicationAdvances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications: part II
Place of PublicationPortugal
PublisherJoão Lita da Silva, Frederico Caeiro, Isabel Natário and Carlos A. Braumann
Pages381-389
ISBN (Print)978-3-642-34903-4/978-3-642-34904-1
Publication statusPublished - 1 Jan 2013

Publication series

NameStudies in Theoretical and Applied Statistics
PublisherJoão Lita da Silva, Frederico Caeiro, Isabel Natário and Carlos A. Braumann

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