Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 104, Issue 487, Pages 1233-1240Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/jasa.2009.tm08458
Keywords
Generalized extreme distribution; Generalized Pareto distribution; Hill estimator; Pareto-type distribution; Tail index regression
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Funding
- NSFC [10771006]
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In extreme value statistics, the tail index is an important measure to gauge the heavy-tailed behavior of a distribution, Under Pareto-type distributions, we employ the logarithmic function to link the tail index to the linear predictor induced by covariates, which constitutes the tail index regression model. We then propose an approximate log-likelihood function to obtain regression parameter estimators, and Subsequently show the asymptotic normality of those estimators. Numerical studies are presented to illustrate theoretical findings.
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