Extreme value theory for dependent sequences via the Stein-Chen method of Poisson approximation (Q1113170)

\textit{L. H. Y. Chen} [Ann. of Probab. 3, 534-545 (1975; Zbl 0335.60016)] extended Stein's method for obtaining error estimates in central limit approximation problems to Poisson approximations. One of the examples he considered was that of a stationary, \(\phi\)-mixing sequence of indicator random variables. In this paper, the author goes more deeply into the problem, in the context of indicators of extreme values in a random sequence. In particular, the error estimates he obtains involve the quantities appearing in the D and D' conditions of dependent extreme value theory. Compound Poisson limit results are also obtained, when stronger local dependence is present.