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.

中文翻译：

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具有可变秩的单变量和双变量顺序统计的极限定理

在这项工作中，我们通过使用降序原则（R 排序）来研究双变量数据的中间和中心顺序统计的渐近行为。当使用超范数时，我们揭示了 R 排序原则和边际排序原则（M 排序）之间的相互关系。完全确定了基于 sup-norms 的中间和中心二元阶统计量的渐近行为。此外，我们强调了归一化常数在表征订单统计的极限类型方面的作用，并给出了有关中间订单统计的新结果。