Robust estimation of the generalized Pareto distribution (Q1848521)

A median estimator is constructed for the parameters \(\gamma\), \(\sigma\) of the generalized Pareto distribution \(F(x)=1-(1+\gamma x/\sigma)^{-1/\gamma}\) by i.i.d. samples. Asymptotic normality of the estimator is demonstrated and the limit covariance matrix is evaluated. Results of simulations are presented where the MLE, the optimal bias robust estimator and the median estimator are compared.