Estimation of the tail index for lattice-valued sequences

Muneya Matsui; Thomas Valentin Mikosch; Laleh Tafakori

doi:10.1007/s10687-012-0167-9

Estimation of the tail index for lattice-valued sequences

Muneya Matsui, Thomas Valentin Mikosch, Laleh Tafakori

Institut for Matematiske Fag

2 Citationer (Scopus)

Abstract

If one applies the Hill, Pickands or Dekkers–Einmahl–de Haan estimators
of the tail index of a distribution to data which are rounded off one often observes that
these estimators oscillate strongly as a function of the number k of order statistics
involved.We study this phenomenon in the case of a Pareto distribution. We provide
formulas for the expected value and variance of the Hill estimator and give bounds on
k when the central limit theorem is still applicable. We illustrate the theory by using
simulated and real-life data.

Originalsprog	Engelsk
Tidsskrift	Extremes
Vol/bind	16
Sider (fra-til)	429-455
ISSN	1386-1999
DOI	https://doi.org/10.1007/s10687-012-0167-9
Status	Udgivet - dec. 2013

Adgang til dokumentet

10.1007/s10687-012-0167-9

Citationsformater

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abstract = "If one applies the Hill, Pickands or Dekkers–Einmahl–de Haan estimatorsof the tail index of a distribution to data which are rounded off one often observes thatthese estimators oscillate strongly as a function of the number k of order statisticsinvolved.We study this phenomenon in the case of a Pareto distribution. We provideformulas for the expected value and variance of the Hill estimator and give bounds onk when the central limit theorem is still applicable. We illustrate the theory by usingsimulated and real-life data.",

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T1 - Estimation of the tail index for lattice-valued sequences

AU - Matsui, Muneya

AU - Mikosch, Thomas Valentin

AU - Tafakori, Laleh

PY - 2013/12

Y1 - 2013/12

N2 - If one applies the Hill, Pickands or Dekkers–Einmahl–de Haan estimatorsof the tail index of a distribution to data which are rounded off one often observes thatthese estimators oscillate strongly as a function of the number k of order statisticsinvolved.We study this phenomenon in the case of a Pareto distribution. We provideformulas for the expected value and variance of the Hill estimator and give bounds onk when the central limit theorem is still applicable. We illustrate the theory by usingsimulated and real-life data.

AB - If one applies the Hill, Pickands or Dekkers–Einmahl–de Haan estimatorsof the tail index of a distribution to data which are rounded off one often observes thatthese estimators oscillate strongly as a function of the number k of order statisticsinvolved.We study this phenomenon in the case of a Pareto distribution. We provideformulas for the expected value and variance of the Hill estimator and give bounds onk when the central limit theorem is still applicable. We illustrate the theory by usingsimulated and real-life data.

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DO - 10.1007/s10687-012-0167-9

M3 - Journal article

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EP - 455

JO - Extremes

JF - Extremes

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