A location invariant moment-type estimator. I

Cheng Xiu Ling; Zuoxiang Peng; Saralees Nadarajah

doi:10.1090/S0094-9000-08-00728-X

A location invariant moment-type estimator. I

Cheng Xiu Ling, Zuoxiang Peng, Saralees Nadarajah

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

4 Citations (Scopus)

Abstract

The moment’s estimator (Dekkers et al., 1989) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves, 2001) is only suitable to estimate 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 estimator, but is made location invariant by a random shift. Its weak consistency and strong consistency are derived, in a semiparametric setup.

Original language	English
Pages (from-to)	23-31
Number of pages	9
Journal	Theory of Probability and Mathematical Statistics
Volume	76
DOIs	https://doi.org/10.1090/S0094-9000-08-00728-X
Publication status	Published - 2008
Externally published	Yes

Keywords

Extreme value index
Location invariant property
Moment estimation
Order statistics
Regular varying functions
Strong and weak consistencies

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10.1090/S0094-9000-08-00728-X

Cite this

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AB - The moment’s estimator (Dekkers et al., 1989) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves, 2001) is only suitable to estimate 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 estimator, but is made location invariant by a random shift. Its weak consistency and strong consistency are derived, in a semiparametric setup.

KW - Extreme value index

KW - Location invariant property

KW - Moment estimation

KW - Order statistics

KW - Regular varying functions

KW - Strong and weak consistencies

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EP - 31

JO - Theory of Probability and Mathematical Statistics

JF - Theory of Probability and Mathematical Statistics

ER -

A location invariant moment-type estimator. I

Abstract

Keywords

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