Estimation of the generalized Pareto distribution

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Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution (2016, unknown): “(9) A “bias-corrected” MLE for θ can then be obtained as: θ̃ = θ̂ − K̂−1Â vec(K̂−1), (10) where K̂ = (K)| θ̂ and Â = (A)| θ̂ , and the bias of θ̃ is O(n−2).”
Fat-Tailed Models for Risk Estimation (2011, background): “The fact that the choice of this threshold has a great impact on the parameter estimates of GPD and, therefore, on the final risk estimates in smaller samples is acknowledged by Goldberg, Miller, and Weinstein as well as by Del Castillo and Daoudi [2008]. In using GPD, one is always faced with the c”