Extreme value theory for dependent sequences via the stein-chen method of poisson approximation

In 1970 Stein introduced a new method for bounding the approximation error in central limit theory for dependent variables. This was subsequently developed by Chen for Poisson approximation and has proved very successful in the areas to which it has been applied. Here we show how the method can be applied to extreme value theory for dependent sequences, focussing particularly on the nonstationary case. The method gives new and shorter proofs of some known results, with explicit bounds for the approximation error.