Bias reduction and explicit semi-parametric estimation of the tail index

✍ Scribed by M.Ivette Gomes; M.João Martins

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 737 KB
• Volume: 124
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(03)00205-2

✦ Synopsis

In this paper, and in a context of regularly varying tails, we analyse particular but interesting cases of the maximum likelihood and least squares estimators proposed by Feuerverger and Hall (Ann. Statist. 27 (1999) 760). All these estimators are alternatives to a well-known estimator of the tail index, the Hill estimator (Ann. Statist. 3 (1997) 1163), and jointly with the generalized jackknife estimators in Gomes et al. (Extremes 2 (2000) 207, Portug. Math. 59 (2002) 393) have essentially in mind a reduction in bias, preferably without increasing mean squared error, leading to semi-parametric estimators of the tail index with a better performance than the classical estimators, provided we may use extreme-value data relatively deep into the sample.