Tail Index Estimation, Pareto Quantile Plots Regression Diagnostics

Jan Beirlant · Petra Vynckier · Jozef L. Teugels

223 citations0/0 files storedJournal of the American Statistical Association

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Probability and Risk Models Statistical Distribution Estimation and Applications Statistical Methods and Inference

Abstract

Successful application of extreme value statistics for estimating the Pareto tail index relies heavily on the choice of the number of extreme values taken into account. It is shown that these tail index estimators can be considered estimates of the slope at the right upper tail of a Pareto quantile plot, obtained using a weighted least squares algorithm. From this viewpoint, based on classical ideas on regression diagnostics, algorithms can be constructed searching for that order statistic to the right of which one obtains an optimal linear fit of the quantile plot.

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References

1989A Moment Estimator for the Index of an Extreme-Value Distribution 1982On Some Simple Estimates of an Exponent of Regular Variation 1985Kernel Estimates of the Tail Index of a Distribution

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2014Extreme Value Theory and Statistics of Univariate Extremes: A Review 2002“Asymptotically Unbiased” Estimators of the Tail Index Based on External Estimation of the Second Order Parameter 2003Diagnostics for Dependence within Time Series Extremes 2001The Bootstrap Methodology in Statistics of Extremes—Choice of the Optimal Sample Fraction 2001A Diagnostic for Selecting the Threshold in Extreme Value Analysis 2000Distribution and Dependence-Function Estimation for Bivariate Extreme-Value Distributions 1996Excess Functions and Estimation of the Extreme-Value Index 2009Tail Index Regression

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