One of the major interests in extreme-value statistics is to infer the tail properties of the distribution functions in the domains of attraction of an extreme-value distribution and predict rare events. There is the primary problem to find the estimation of the tail index γ, usually performed on the basis of the largest k order statistics in the sample. The question that has been often solved in applications of extreme value theory is the choice of k or an estimation of γ. We shall be here mainly interested in the use of the bootstrap methodology to estimate Extreme Value Index (EVI) γ. We study and compute general case of this tail index γ. We shall also compare, through Monte Carlo simulation, these bootstrap methodologies with other data - driven choices of the optimal sample fraction.
展开▼
