Modified martingale difference correlations

Jingke Zhou, Lixing Zhu*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)359-386
Number of pages28
JournalJournal of Nonparametric Statistics
Volume33
Issue number2
DOIs
Publication statusPublished - 23 Jun 2021

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • 62H20
  • Conditional mean independence
  • distance correlation
  • martingale difference correlation
  • partial correlation
  • variable screening

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