“Asymptotically Unbiased” Estimators of the Tail Index Based on External Estimation of the Second Order Parameter

By M. Ivette Gomesa, M. J. Martins. 2002

174 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e68ea04cd93827ec46534a2cd5cc3ef98cf10cec

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Citations in the corpus

A Sturdy Reduced-Bias Extreme Quantile (VaR) Estimator (2007, background): “…moment of the underlying X. 3.5 Extreme Quantile or VaR Estimators Gomes and Figueiredo (2006) suggested the use in (1.2) of the second-order reduced-bias tail index estimators in Gomes and Martins (2001, 2002) and Gomes, Caeiro, and Figueiredo (2004a), with an asymptotic variance σ 2R > γ 2.”
Improved reduced-bias tail index and quantile estimators (2008, methodology): “From Gomes and Martins (2004), we know that if second-order condition U ∈ R and k is an intermediate sequence, then”
DIRECT REDUCTION OF BIAS OF THE CLASSI- CAL HILL ESTIMATOR ⁄ (2005, background): “Such a decision is related to the discussion in Gomes and Martins (2002) on the advantages of an external estimation of the second order parameter ρ (or even their misspecification, as in Gomes and Martins (2004)) versus an internal estimation at the same level k.”
Second-order refined peaks-over-threshold modelling for heavy-tailed distributions (2009, methodology): “complicates both theory and computations. Bias-reduction methodshave already beenproposedin, amongstothers, Feuerverger and Hall (1999),Gomes et al.(2000),Beirlant et al.(1999),Beirlant et al.(2002a),Gomes and Martins (2002), and Gomes and Martins (2004). These methods focus on the distribution of l”
Statistics of Extremes (2004, background): “Gumbel and Goldstein (1964) already investigate the maximum annual discharges of the Ocmulgee River in Georgia at two different stations located upstream and downstream.”
A new class of estimators of a “scale” second order parameter (2007, background): “11, the estimator of β obtained in Gomes and Martins (2002), given by”
Threshold Selection in Extreme Value Analysis (2016, background): “The problem of excessive oscillation of the Hill EVI-estimator has been discussed by Resnick and Stărică ([47]), who recommend the smoothing of the Hillestimator by integrating it over a moving window (see also, Resnick, [49] and Martins, Gomes and Neves, [43]).”