Location invariant Weiss-Hill estimator

Chengxiu Ling; Zuoxiang Peng; Saralees Nadarajah

doi:10.1007/s10687-011-0134-x

Location invariant Weiss-Hill estimator

Chengxiu Ling, Zuoxiang Peng, Saralees Nadarajah^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

In this paper, a new kind of location invariant Weiss-Hill estimator of the extreme value index γ ∈ ℝ is proposed. The new estimator is a combination of two estimators proposed by Weiss (Nav Res Logist Q 1:111-114, 1971) and Fraga Alves (Extremes 4:199-217, 2001a). The following properties of the new estimator are derived: weak consistency, strong consistency, and asymptotic expansions. A bias corrected version of the proposed estimator is given after determining an optimal sample fraction. Some finite simulation studies are performed.

Original language	English
Pages (from-to)	197-230
Number of pages	34
Journal	Extremes
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/s10687-011-0134-x
Publication status	Published - Jun 2012
Externally published	Yes

Keywords

Extreme value index
Location invariant
Mean squared error
Second order regular variation

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10.1007/s10687-011-0134-x

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abstract = "In this paper, a new kind of location invariant Weiss-Hill estimator of the extreme value index γ ∈ ℝ is proposed. The new estimator is a combination of two estimators proposed by Weiss (Nav Res Logist Q 1:111-114, 1971) and Fraga Alves (Extremes 4:199-217, 2001a). The following properties of the new estimator are derived: weak consistency, strong consistency, and asymptotic expansions. A bias corrected version of the proposed estimator is given after determining an optimal sample fraction. Some finite simulation studies are performed.",

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AU - Nadarajah, Saralees

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AB - In this paper, a new kind of location invariant Weiss-Hill estimator of the extreme value index γ ∈ ℝ is proposed. The new estimator is a combination of two estimators proposed by Weiss (Nav Res Logist Q 1:111-114, 1971) and Fraga Alves (Extremes 4:199-217, 2001a). The following properties of the new estimator are derived: weak consistency, strong consistency, and asymptotic expansions. A bias corrected version of the proposed estimator is given after determining an optimal sample fraction. Some finite simulation studies are performed.

KW - Extreme value index

KW - Location invariant

KW - Mean squared error

KW - Second order regular variation

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Location invariant Weiss-Hill estimator

Abstract

Keywords

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