Μοντέλα εκτίμησης του δείκτη ακραίων τιμών και αξιολόγηση τους
A review of methods for tail index estimation
The extreme value theory consists of the probabilistic theoretical framework for the study of models in which sample values are considered to be extreme (e.g. very large claims, large stock price fluctuations, extreme values of environmental measurements, extreme geological or weather phenomena). One of the main aims of this theory is the determination of the shape of the right (or left) tail of the data distribution, so that long-term prediction of extreme observations can be efficiently achieved. The shape of the right tail of a distribution is characterized by the tail index 𝜉, whose value identifies a more or less heavy tail. The purpose of this dissertation is to present a review of well known methods for estimating this parameter. In particular we are interested in Hill’s Estimator, Negative Hill’s Estimator, Pickand’s Estimator, MLE Estimator, Moments Estimator, Moments Ratio Estimator, Peng Estimator, W Estimator and PWM Estimator. We compare the effectiveness of these estimators either analytically or, mainly, through Monte Carlo simulation (for this purpose R software will be used).