Kernel Estimates of the Tail Index of a Distribution

Sándor Csörgő · Paul Deheuvels · David M. Mason

283 citations0/0 files storedThe Annals of Statistics

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Probability and Risk Models Probability and Statistical Research Statistical Methods and Inference

Abstract

We introduce a new estimate of the exponent of a distribution whose tail varies regularly at infinity. This estimate is expressed as the convolution of a kernel with the logarithm of the quantile function, and includes as particular cases the estimates introduced by Hill and by De Haan. Under very weak conditions, we prove asymptotic normality, consistency and discuss the optimal choices of the kernel and of the bandwidth parameter.

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1997The variation of certain speculative prices 1982On Some Simple Estimates of an Exponent of Regular Variation

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1999Tail Index Estimation and an Exponential Regression Model 1998Selecting the optimal sample fraction in univariate extreme value estimation 1999Estimating a tail exponent by modelling departure from a Pareto distribution 1996Tail Index Estimation, Pareto Quantile Plots Regression Diagnostics 1996The qq-estimator and heavy tails 2014Extreme Value Theory and Statistics of Univariate Extremes: A Review 1997Smoothing the Hill Estimator 2006Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents

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