A functional law of the iterated logarithm for kernel-type estimators of the tail index |
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| Institution: | 1. Department of Management, University of Toronto Scarborough, Toronto, Canada;2. Departamento de Análisis Económico, Universidad de Zaragoza, Zaragoza, Spain;1. Saint Petersburg State University, Saint Petersburg, 199034 Russia;2. Saint Petersburg State Transport University, Saint Petersburg, 190031 Russia;3. Purdue University, West Lafayette, IN 47907, United States;4. Risk and Insurance Studies Centre, York University, Toronto, Ontario M3J 1P3, Canada;5. Western University, London, Ontario N6A 5B7, Canada;1. IBM Research, T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA;2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada |
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| Abstract: | Under von Mises's condition, the kernel tail index estimators of Csörgő et al. (Ann. Statist. 13 (1985) 1050) have been generalized by Groeneboon et al. (Ann. Statist. 31 (2003) 1956) for all real tail indices. Weak consistency and asymptotic normality of their kernel estimators have been established. In this paper, we present a characterization of the almost sure behavior of these estimators and we show their strong consistency. |
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