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

Department of Mathematical Sciences

2 Citations (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.

Original language	English
Journal	Extremes
Volume	16
Pages (from-to)	429-455
ISSN	1386-1999
DOIs	https://doi.org/10.1007/s10687-012-0167-9
Publication status	Published - Dec 2013

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10.1007/s10687-012-0167-9

Cite this

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title = "Estimation of the tail index for lattice-valued sequences",

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

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