Abstract
We introduce the partial martingale difference correlation, a scalar-valued measure of conditional mean dependence of Y given X, adjusting for the nonlinear dependence on Z, where X, Y and Z are random vectors of arbitrary dimensions. At the population level, partial martingale difference correlation is a natural extension of partial distance correlation developed recently by Székely and Rizzo [14], which characterizes the dependence of Y and X, after controlling for the nonlinear effect of Z. It extends the martingale difference correlation first introduced in Shao and Zhang [10] just as partial distance correlation extends the distance correlation in Székely, Rizzo and Bakirov [13]. Sample partial martingale difference correlation is also defined building on some new results on equivalent expressions of sample martingale difference correlation. Numerical results demonstrate the effectiveness of these new dependence measures in the context of variable selection and dependence testing.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1492-1517 |
| Number of pages | 26 |
| Journal | Electronic Journal of Statistics |
| Volume | 9 |
| DOIs | |
| State | Published - Jan 1 2015 |
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Keywords
- Distance correlation
- Nonlinear dependence
- Partial correlation
- Variable selection
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Partial martingale difference correlation. / Park, Trevor H; Shao, Xiaofeng; Yao, Shun.
In: Electronic Journal of Statistics, Vol. 9, 01.01.2015, p. 1492-1517.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Partial martingale difference correlation
AU - Park, Trevor H
AU - Shao, Xiaofeng
AU - Yao, Shun
PY - 2015/1/1
Y1 - 2015/1/1
N2 - We introduce the partial martingale difference correlation, a scalar-valued measure of conditional mean dependence of Y given X, adjusting for the nonlinear dependence on Z, where X, Y and Z are random vectors of arbitrary dimensions. At the population level, partial martingale difference correlation is a natural extension of partial distance correlation developed recently by Székely and Rizzo [14], which characterizes the dependence of Y and X, after controlling for the nonlinear effect of Z. It extends the martingale difference correlation first introduced in Shao and Zhang [10] just as partial distance correlation extends the distance correlation in Székely, Rizzo and Bakirov [13]. Sample partial martingale difference correlation is also defined building on some new results on equivalent expressions of sample martingale difference correlation. Numerical results demonstrate the effectiveness of these new dependence measures in the context of variable selection and dependence testing.
AB - We introduce the partial martingale difference correlation, a scalar-valued measure of conditional mean dependence of Y given X, adjusting for the nonlinear dependence on Z, where X, Y and Z are random vectors of arbitrary dimensions. At the population level, partial martingale difference correlation is a natural extension of partial distance correlation developed recently by Székely and Rizzo [14], which characterizes the dependence of Y and X, after controlling for the nonlinear effect of Z. It extends the martingale difference correlation first introduced in Shao and Zhang [10] just as partial distance correlation extends the distance correlation in Székely, Rizzo and Bakirov [13]. Sample partial martingale difference correlation is also defined building on some new results on equivalent expressions of sample martingale difference correlation. Numerical results demonstrate the effectiveness of these new dependence measures in the context of variable selection and dependence testing.
KW - Distance correlation
KW - Nonlinear dependence
KW - Partial correlation
KW - Variable selection
UR - http://www.scopus.com/inward/record.url?scp=84937856954&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84937856954&partnerID=8YFLogxK
U2 - 10.1214/15-EJS1047
DO - 10.1214/15-EJS1047
M3 - Article
VL - 9
SP - 1492
EP - 1517
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
ER -