The consistency of the jackknife estimator of the asymptotic covariance matrix of a differentiable function of the symmetrized Tyler matrix is proved for sampling from continuous distribution without any constraint on this sampled continuous distribution. It is shown that under mild regularity conditions the rank of the asymptotic covariance matrix attains maximum possible value. The results are applied to the construction of the asymptotic confidence interval for correlation coefficient. It is illustrated by simulations that for some distributions the proposed interval yields better results than the classical Z-transformation interval.

中文翻译：

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关于对称的泰勒矩阵

证明了对称的泰勒矩阵的微分函数的渐近协方差矩阵的前刀估计的一致性，可以从连续分布中进行采样，而对该采样的连续分布没有任何约束。结果表明，在轻度规律性条件下，渐近协方差矩阵的秩达到最大可能值。将结果应用于相关系数的渐近置信区间的构建。通过仿真表明，对于某些分布，建议的间隔比经典的Z变换间隔产生更好的结果。