To ameliorate some drawbacks of Martingale Difference Correlation (MDC) such as the asymmetry in the sense that for a pair of vectors, the value of MDC may not be equal to 1, and the self-MDC of any random vector can be different from vector to vector in value, we in this paper propose a modified MDC (MMDC). Further, as the corresponding partial MDC (PMDC), with controlling another random vector, cannot ensure the equivalence between conditional mean independence and zero PMDC, we then also propose a modified partial MDC (MPMDC) to guarantee, under some regularity conditions, the equivalence. We further investigate the theoretical properties of the corresponding unbiased estimators and apply them to variable screening and hypothesis testing. Numerical studies and real data analysis are conducted to examine their finite sample performances.

为了改善 Martingale Difference Correlation (MDC) 的一些缺点，例如不对称性，对于一对向量，MDC的值可能不等于 1，而自MDC任何随机向量的值都可以从向量到向量不同，我们在本文中提出了一种改进的 MDC（MMDC）。此外，由于相应的部分 MDC（PMDC），控制另一个随机向量，不能保证条件平均独立性和零 PMDC 之间的等价性，我们还提出了一个修改的部分 MDC（MPMDC）来保证在某些规律性条件下，等价性. 我们进一步研究了相应的无偏估计量的理论特性，并将它们应用于变量筛选和假设检验。进行数值研究和实际数据分析以检查它们的有限样本性能。