Tail Index Regression

• 成果类型: Article
• 署名作者: Wang, Hansheng; Tsai, Chih-Ling
• 署名单位: Peking University; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08458
• 发表日期: 2009
• 页码: 1233-1240
• 关键词: regular variation; hill estimator; selection; exponent; models

摘要

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.