论文标题
依赖数据的经验距离协方差的渐近行为
Asymptotic Behaviour of the Empirical Distance Covariance for Dependent Data
论文作者
论文摘要
我们为可分离的度量空间的经验距离协方差提供了两个渐近结果，而对样品没有任何IID假设。特别是，只要样品形成严格的固定且千古的过程，我们就显示了任何度量的经验距离协方差几乎确定的融合。我们进一步给出了关于在样品绝对规律性的假设下经验距离协方差的渐近分布的结果，并将这些结果扩展到某些类型的伪空间。在此过程中，我们得出了一个有关在较强的混合条件下阶数2的渐近V统计量的渐近分布的一般定理。
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any measure with finite first moments, provided that the samples form a strictly stationary and ergodic process. We further give a result concerning the asymptotic distribution of the empirical distance covariance under the assumption of absolute regularity of the samples and extend these results to certain types of pseudometric spaces. In the process, we derive a general theorem concerning the asymptotic distribution of degenerate V-statistics of order 2 under a strong mixing condition.
