Limit theorems for univariate and bivariate order statistics with variable ranks

In this work, we investigate the asymptotic behaviour of the intermediate and central order statistics of a bivariate 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 behaviour of the intermediate and central bivariate order statistics based on sup-norms is completely determined. Besides, we highlight the role of the normalizing constants in characterizing the limit types of order statistics and new results concerning the intermediate order statistics are given.