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Tail And Nontail Memory With Applications To Extreme Value And Robust Statistics

Listed author(s):
  • Hill, Jonathan B.

New notions of tail and nontail dependence are used to characterize separately extremal and nonextremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove that near epoch dependence (McLeish, 1975; Gallant and White, 1988) and L 0 -approximability (Pötscher and Prucha, 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general conditions. We apply the theory to characterize the extremal and nonextremal memory properties of possibly very heavy-tailed GARCH processes and distributed lags. This in turn is used to verify Gaussian limits for tail index, tail dependence, and tail-trimmed sums of these data, allowing for Gaussian asymptotics for a new tail-trimmed least squares estimator for heavy-tailed processes.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 04 (August)
Pages: 844-884

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Handle: RePEc:cup:etheor:v:27:y:2011:i:04:p:844-884_00
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