In this work, we investigate the asymptotic behavior of the extremes of a multivariate data by using the Reduced Ordering Principle (R-ordering). When, the sup-norm is used, we reveal the interrelation between the R-ordering principle and Marginal Ordering Principle (M-ordering). The asymptotic behavior of the maximum sup-norms corresponding to the bivariate data is completely determined. Finally, an application to real data illustrates and corroborates the theoretical results.
H. M. Barakat. E. M. Nigm. M. H. Harpy. "Asymptotic behavior of the maximum of multivariate order statistics in a norm sense." Braz. J. Probab. Stat. 34 (4) 868 - 884, October 2020. https://doi.org/10.1214/19-BJPS465