pmdd function

Partial Martingale Difference Divergence

pmdd measures conditional mean dependence of Y given X adjusting for the dependence on Z, where each contains one variable (univariate) or more variables (multivariate). Only the U-centering approach is applied.

pmdd(X, Y, Z)

Arguments

• X: A vector, matrix or data frame, where rows represent samples, and columns represent variables.
• Y: A vector, matrix or data frame, where rows represent samples, and columns represent variables.
• Z: A vector, matrix or data frame, where rows represent samples, and columns represent variables.

Returns

pmdd returns the squared partial martingale difference divergence of Y given X adjusting for the dependence on Z.

Examples

# X, Y, Z are vectors with 10 samples and 1 variable
X <- rnorm(10)
Y <- rnorm(10)
Z <- rnorm(10)

pmdd(X, Y, Z)

# X, Y, Z are 10 x 2 matrices with 10 samples and 2 variables
X <- matrix(rnorm(10 * 2), 10, 2)
Y <- matrix(rnorm(10 * 2), 10, 2)
Z <- matrix(rnorm(10 * 2), 10, 2)

pmdd(X, Y, Z)

References

Park, T., Shao, X., and Yao, S. (2015). Partial martingale difference correlation. Electronic Journal of Statistics, 9(1), 1492-1517. http://dx.doi.org/10.1214/15-EJS1047.