On blocks and runs estimators of the extremal index |
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| Institution: | 1. Human Development & Family Studies, Pennsylvania State University, University Park, PA 16802, United States;2. Criminology & Sociology, Pennsylvania State University, University Park, PA 16802, United States;3. Institute for Translational Research & Institute of Child Development, University of Minnesota, Minneapolis, MN 55414, United States;4. Department of Social Welfare, University of California—Los Angeles, Los Angeles, CA 90095, United States |
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| Abstract: | 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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