Can you explain in more detail why this can't be updated online? We can track the rank of newly sampled pairs in LogN using something like an order statistic t

Can you explain in more detail why this can't be updated online? We can track the rank of newly sampled pairs in LogN using something like an order statistic tree: https://en.wikipedia.org/wiki/Order_statistic_tree https://en.wikipedia.org/wiki/Order_statistic_tree But I guess the problem is that with each new pair, O(n) pairs could change their contribution to the correlation coefficient.