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On blocks and runs estimators of the extremal index

✍ Scribed by I. Weissman; S.Yu. Novak

Book ID
104340469
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
301 KB
Volume
66
Category
Article
ISSN
0378-3758

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✦ Synopsis

Given a sample from a stationary sequence of random variables, we study the blocks and runs estimators of the extremal index. Conditions are given for consistency and asymptotic normality of these estimators. We show that moment restrictions assumed by Hsing (Stochast. Process. Appl. 37(1), 117 139; Ann. Statist. 21(4), 2043-2021) may be relaxed if a stronger mixing condition holds. The CLT for the runs estimator seems to be proven for the first time.

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We consider the class of estimators of the extreme value index [~ that can be represented as a scale invariant functional T applied to the empirical tail quantile function Q,. From an approximation of Q,, first asymptotic normality of T(Q~) is derived under quite natural smoothness conditions on 7"