Ornstein Petra, Lyhagen Johan
Department of Statistics, Uppsala University, Uppsala, Sweden.
PLoS One. 2016 Jan 5;11(1):e0145595. doi: 10.1371/journal.pone.0145595. eCollection 2016.
The asymptotic variance and distribution of Spearman's rank correlation have previously been known only under independence. For variables with finite support, the population version of Spearman's rank correlation has been derived. Using this result, we show convergence to a normal distribution irrespectively of dependence, and derive the asymptotic variance. A small simulation study indicates that the asymptotic properties are of practical importance.
斯皮尔曼等级相关系数的渐近方差和分布此前仅在独立性假设下为人所知。对于具有有限支撑的变量，已推导出斯皮尔曼等级相关系数的总体形式。利用这一结果，我们证明了无论变量间是否相关，其均收敛于正态分布，并推导出了渐近方差。一项小型模拟研究表明，这些渐近性质具有实际重要性。
