论文标题
根据渐近方差的基于相关的一致性的比较
Comparison of correlation-based measures of concordance in terms of asymptotic variance
论文作者
论文摘要
我们将出现的一致性度量比较为Pearson的线性相关系数在两个随机变量之间转换，以便它们遵循所谓的一致性诱导分布。这种转变的等级相关类别包括Spearman的Rho，Blomqvist的Beta和Van der Waerden的系数。当仅需要一致性的标准公理时，并不总是清楚哪种转换的等级相关最适合使用。为了解决这个问题，我们根据某些规范估计量的最佳和最差的渐近方差比较了一致的一致性方差。从这种方法中得出的一个简单标准是，与第四次较小的诱导一致性诱导分布更可取。特别是，我们表明，Blomqvist的Beta是从这个意义上讲是最佳转换的等级相关性，而Spearman的Rho的表现优于Van der Waerden的系数。此外，我们发现肯德尔（Kendall）的tau与Blomqvist的beta相关，尽管它不是该性质的转变等级相关性，但它与Blomqvist的Beta具有一定的最佳结构。
We compare measures of concordance that arise as Pearson's linear correlation coefficient between two random variables transformed so that they follow the so-called concordance-inducing distributions. The class of such transformed rank correlations includes Spearman's rho, Blomqvist's beta and van der Waerden's coefficient. When only the standard axioms of measures of concordance are required, it is not always clear which transformed rank correlation is most suitable to use. To address this question, we compare measures of concordance in terms of their best and worst asymptotic variances of some canonical estimators over a certain set of dependence structures. A simple criterion derived from this approach is that concordance-inducing distributions with smaller fourth moment are more preferable. In particular, we show that Blomqvist's beta is the optimal transformed rank correlation in this sense, and Spearman's rho outperforms van der Waerden's coefficient. Moreover, we find that Kendall's tau, although it is not a transformed rank correlation of that nature, shares a certain optimal structure with Blomqvist's beta.
