TY - JOUR
T1 - Modified martingale difference correlations
AU - Zhou, Jingke
AU - Zhu, Lixing
N1 - The research described herewith was supported by a grant from the University Grants Council of Hong Kong and NSFC grants [NSFC 11671042 and NSFC 71801137]. The authors greatly appreciate the thorough and thought-provoking reviews by two referees and an Associate Editor, which contain many useful suggestions and lead to substantial improvements of this work. The authors are also grateful to Prof. Xiaofeng Shao for his constructive comments that led to a substantial improvement of the article.
Publisher Copyright:
© 2021 American Statistical Association and Taylor & Francis.
PY - 2021/6/23
Y1 - 2021/6/23
N2 - 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.
AB - 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.
KW - 62H20
KW - Conditional mean independence
KW - distance correlation
KW - martingale difference correlation
KW - partial correlation
KW - variable screening
UR - http://www.scopus.com/inward/record.url?scp=85108316816&partnerID=8YFLogxK
U2 - 10.1080/10485252.2021.1941951
DO - 10.1080/10485252.2021.1941951
M3 - Journal article
AN - SCOPUS:85108316816
SN - 1048-5252
VL - 33
SP - 359
EP - 386
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
IS - 2
ER -