We present efficient algorithms for simultaneously computing Kendall's tau and the jackknife estimator of its variance. For the classical pairwise tau, we describe a modification of Knight's algorithm (originally designed to compute only tau) that does so while preserving its $O(n \log_2 n)$ runtime in the number of observations $n$. We also introduce a novel algorithm computing a multivariate extension of tau and its jackknife variance in $O(n \log_2^p n)$ time.

翻译：本文提出了同步计算Kendall's tau及其刀切法方差估计量的高效算法。针对经典配对tau，我们描述了Knight算法（原设计仅用于计算tau）的改进版本，该算法在保持$O(n \log_2 n)$时间复杂度的同时实现了同步计算，其中$n$为观测值数量。此外，我们提出了一种创新算法，可在$O(n \log_2^p n)$时间内计算tau的多变量扩展形式及其刀切法方差。