Modified martingale difference correlations

摘要

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.