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Asymptotic Mean and Variance of Gini Correlation for Bivariate Normal Samples

机译:二元正态样本的基尼相关性的渐近均值和方差

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This paper derives the asymptotic analytical forms of the mean and variance of the Gini correlation (GC) with respect to samples drawn from bivariate normal populations. The asymptotic relative efficiency (ARE) of the Gini correlation to Pearson's product moment correlation coefficient (PPMCC) is investigated under the normal assumptions. To gain further insight into GC, we also compare the Gini correlation to other two closely related correlation coefficients, namely, the order statistics correlation coefficient (OSCC) and Spearman's rho (SR). Theoretical and simulation results suggest that the performance of GC lies in between those of OSCC and SR when estimating the correlation coefficient of the bivariate normal population. The newly found theoretical results along with other desirable properties enable GC to be a useful alternative to the existing coefficients, especially when one wants to make a trade-off between the efficiency and robustness to monotone nonlinearity.
机译:本文从二元正态总体中得出样本的基尼相关(GC)平均值和方差的渐近分析形式。在正常假设下,研究了基尼相关性与皮尔逊产品动量相关性系数(PPMCC)的渐近相对效率(ARE)。为了进一步了解GC,我们还将基尼相关性与其他两个密切相关的相关系数进行了比较,即阶数统计相关系数(OSCC)和Spearman的rho(SR)。理论和模拟结果表明,当估计双变量正态总体的相关系数时,GC的性能介于OSCC和SR之间。新近发现的理论结果以及其他理想的特性使GC可以替代现有系数,尤其是当要在效率和鲁棒性之间权衡单调非线性时。

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