A location invariant moment-type estimator. II. (English) Zbl 1193.62053

Ling, Cheng-Xiu; Peng, Zuoxiang; Nadarajah, Saralees

Teor. Jmovirn. Mat. Stat. 77, 149-160 (2007) and Theory Probab. Math. Stat. 77, 177-189 (2008).

In the first part of this paper [ibid. 76, 22–30 (2007; Zbl 1193.62052)] an estimator for the tail index \(\gamma\in\mathbb R\) based on an invariant Hill type estimator and a moment-type estimator was proposed. The weak and strong consistency of this new estimator were derived. In this paper, the asymptotic normality of the estimator is derived in a semiparametric set up.

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

62G05	Nonparametric estimation
62G20	Asymptotic properties of nonparametric inference

Keywords:

extreme value index; location invariant property; moment estimation, strong and weak consistency; order statistics; regular varying functions

Citations:

Zbl 1193.62052