Bias - Corrected Maximum Likelihood Estimation of the Parameters of the Generalized Pareto Distribution

We derive analytic expressions for the biases, to O(n-1), of the maximum likelihood estimators of the parameters of the generalized Pareto distribution. Using these expressions to bias-correct the estimators is found to be extremely effective in terms of bias reduction, and can also result in a small reduction in relative mean squared error. In terms of remaining relative bias, the analytic bias-corrected estimators are somewhat less effective than their counterparts obtained by using a parametric bootstrap bias correction. However, the analytic correction out-performs the bootstrap correction in terms of remaining %MSE. Taking into account the relative computational costs, this leads us to recommend the use of the analytic bias adjustment for most practical situations.