mdd function

Martingale Difference Divergence

mdd measures conditional mean dependence of Y given X, where each contains one variable (univariate) or more variables (multivariate).

mdd(X, Y, compute = "C", center = "U")

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.

• compute: The method for computation, including

  • C: computation implemented in C code;
  • R: computation implemented in R code.

• center: The approach for centering, including

  • U: U-centering which leads to an unbiased estimator;
  • D: double-centering which leads to a biased estimator.

Returns

mdd returns the squared martingale difference divergence of Y given X.

Examples

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

mdd(X, Y, compute = "C")
mdd(X, Y, compute = "R")

# X, Y 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)

mdd(X, Y, center = "U")
mdd(X, Y, center = "D")

References

Shao, X., and Zhang, J. (2014). Martingale difference correlation and its use in high-dimensional variable screening. Journal of the American Statistical Association, 109(507), 1302-1318. http://dx.doi.org/10.1080/01621459.2014.887012.

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.