Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening
By Xiaofeng Shao, Jingsi Zhang. 2014
203 citations recorded by the source corpus.
In this article, we propose a new metric, the so-called martingale difference correlation, to measure the departure of conditional mean independence between a scalar response variable V and a vector predictor variable U. Our metric is a natural extension of distance correlation proposed by Székely, Rizzo, and Bahirov, which is used to measure the dependence between V and U. The martingale difference correlation and its empirical counterpart inherit a number of desirable features of distance correlation and sample distance correlation, such as algebraic simplicity and elegant theoretical properties. We further use martingale difference correlation as a marginal utility to do high-dimensional variable screening to screen out variables that do not contribute to conditional mean of the response given the covariates. Further extension to conditional quantile screening is also described in detail and sure screening properties are rigorously justified. Both simulation results and real data illustrations demonstrate the effectiveness of martingale difference correlation-based screening procedures in comparison with the existing counterparts. Supplementary materials for this article are available online.
Subfields: Molecular Biology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/5e3f52a47734558139f387c51e1cbf36831a1a36
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Citations in the corpus
- An Updated Literature Review of Distance Correlation and Its Applications to Time Series (2017, unknown): “Another related measure is the martingale difference correlation (Shao and Zhang, 2014), which is defined for p Here MDD ( U, V ) denotes the martingale difference divergence given by .”
- Conditional quantile screening in ultrahigh-dimensional heterogeneous data (2015, methodology): “Compared with the finite exponential moment conditions C3 in Zhu et al. (2011), C1 in Li et al. (2012b) and B2 in Shao & Zhang (2014), as well as the bounded support condition C1 in He et al. (2013), we impose no conditions on the predictor Z , so our screening procedures are more robust with…”