Under a second order regular variation condition, rates of convergence of the distribution of bivariate extreme order statistics to its limit distribution are given both in the total variation metric and in the uniform metric.

doi.org/10.1006/jmva.1997.1669, hdl.handle.net/1765/69652
Journal of Multivariate Analysis
Tinbergen Institute

de Haan, L., & Peng, L. (1997). Rates of convergence for bivariate extremes. Journal of Multivariate Analysis, 61(2), 195–230. doi:10.1006/jmva.1997.1669