Rates of Convergence in Extreme Value Theory

If Hn(x) is the exact distribution function of the maximum in a sample of size n and H(x) is a limiting distribution, one can consider |Hn(an+bnx)−H(x)| for fixed x, or its supremum in x on a finite interval, or on the whole real line. The paper discusses these three possibilities. The practical side of these estimates is discussed, and several open questions are raised.