A location invariant moment-type estimator II

Cheng Xiu Ling; Zuoxiang Peng; Saralees Nadarajah

doi:10.1090/S0094-9000-09-00756-X

A location invariant moment-type estimator II

Cheng Xiu Ling, Zuoxiang Peng, Saralees Nadarajah

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

The moment estimator (Dekkers et al. (1989)) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The loca- tion invariant Hill-type estimator (Fraga Alves (2001)) is only suitable for estimating positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type estima- tor, but it is made location invariant by a random shift. Its asymptotic normality is derived, in a semiparametric setup.

Original language	English
Pages (from-to)	177-189
Number of pages	13
Journal	Theory of Probability and Mathematical Statistics
Volume	77
DOIs	https://doi.org/10.1090/S0094-9000-09-00756-X
Publication status	Published - 2008
Externally published	Yes

Keywords

As- ymptotic normality
Extreme value index
Location invariant property
Moment estimation
Order statistics
Regular varying functions

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10.1090/S0094-9000-09-00756-X

Cite this

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AU - Peng, Zuoxiang

AU - Nadarajah, Saralees

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N2 - The moment estimator (Dekkers et al. (1989)) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The loca- tion invariant Hill-type estimator (Fraga Alves (2001)) is only suitable for estimating positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type estima- tor, but it is made location invariant by a random shift. Its asymptotic normality is derived, in a semiparametric setup.

AB - The moment estimator (Dekkers et al. (1989)) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The loca- tion invariant Hill-type estimator (Fraga Alves (2001)) is only suitable for estimating positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type estima- tor, but it is made location invariant by a random shift. Its asymptotic normality is derived, in a semiparametric setup.

KW - As- ymptotic normality

KW - Extreme value index

KW - Location invariant property

KW - Moment estimation

KW - Order statistics

KW - Regular varying functions

UR - https://www.scopus.com/pages/publications/85009774801

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VL - 77

SP - 177

EP - 189

JO - Theory of Probability and Mathematical Statistics

JF - Theory of Probability and Mathematical Statistics

ER -

A location invariant moment-type estimator II

Abstract

Keywords

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