Estimation of the tail index for lattice-valued sequences

Matsui, M, Mikosch, T and Tafakori, L 2013, 'Estimation of the tail index for lattice-valued sequences', Extremes, vol. 16, no. 4, pp. 429-455.


Document type: Journal Article
Collection: Journal Articles

Title Estimation of the tail index for lattice-valued sequences
Author(s) Matsui, M
Mikosch, T
Tafakori, L
Year 2013
Journal name Extremes
Volume number 16
Issue number 4
Start page 429
End page 455
Total pages 27
Publisher Springer
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.
Subject Statistical Theory
Probability Theory
Applied Statistics
Keyword(s) Tail index
Hill estimator
Pickands estimator
DekkersEinmahlde Haan estimator
Discretized Pareto random variable
Central limit theorem
Consistency
DOI - identifier 10.1007/s10687-012-0167-9
Copyright notice © Springer Science+BusinessMedia New York 2013
ISSN 1386-1999
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