  For non-uniformly hyperbolic dynamical systems we consider the time series of
maxima along typical orbits. Using ideas based upon quantitative recurrence
time statistics we prove convergence of the maxima (under suitable
normalization) to an extreme value distribution, and obtain estimates on the
rate of convergence. We show that our results are applicable to a range of
examples, and include new results for Lorenz maps, certain partially hyperbolic
systems, and non-uniformly expanding systems with sub-exponential decay of
correlations. For applications where analytic results are not readily available
we show how to estimate the rate of convergence to an extreme value
distribution based upon numerical information of the quantitative recurrence
statistics. We envisage that such information will lead to more efficient
statistical parameter estimation schemes based upon the block-maxima method.
