Estimation of the tail index for lattice-valued sequences

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...

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Bibliographic Details
Published inExtremes (Boston) Vol. 16; no. 4; pp. 429 - 455
Main Authors Matsui, Muneya, Mikosch, Thomas, Tafakori, Laleh
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.12.2013
Springer Nature B.V
Subjects
Central limit theorem
Civil Engineering
Datasets
Earthquakes
Economics
Environmental Management
Estimating techniques
Estimators
Expected values
Finance
Hydrogeology
Insurance
Management
Mathematics and Statistics
Normal distribution
Pareto optimality
Quality Control
Random variables
Reliability
Safety and Risk
Simulation
Statistical analysis
Statistics
Statistics for Business
Studies
Theorems
Variance
Zipf's Law
Central limit theorem
Primary—62G32; Secondary—62G20
Dekkers–Einmahl–de Haan estimator
Pickands estimator
Consistency
62G30
Discretized Pareto random variable
Tail index
Hill estimator
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-012-0167-9