Improving extreme value statistics

Abstract

The rate of uniform convergence in extreme value statistics is non-universal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme value fit beyond the available data. We show that by using simple nonlinear transformations the extreme value approximation can be rendered rapidly convergent in the bulk, and asymptotic in the tail, thus fixing both issues. The transformations are often parameterized by just one parameter which can be estimated numerically. The classical extreme value method is shown to be a special case of the proposed method. We demonstrate that vastly improved results can be obtained with almost no extra cost.