Smooth tail index estimation
نویسندگان
چکیده
Both parametric distribution functions appearing in extreme value theory the generalized extreme value distribution and the generalized Pareto distribution have log-concave densities if the extreme value index γ ∈ [−1, 0]. Replacing the order statistics in tail index estimators by their corresponding quantiles from the distribution function that is based on the estimated log-concave density f̂n leads to novel smooth quantile and tail index estimators. Monte Carlo simulations suggest that these new estimators are highly accurate and well superior to their non-smoothed counterparts. MSC: Primary 62G32, 62G07; Secondary 60G70
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