mddm {EDMeasure}

Martingale Difference Divergence Matrix

Description

mddm extends martingale difference divergence from a scalar to a matrix. It encodes the linear combinations of all univariate components in Y that are conditionally mean independent of X. Only the double-centering approach is applied.

Usage

mddm(X, Y, compute = "C")

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.

Value

mddm returns the martingale difference divergence matrix of Y given X.

References

Lee, C. E., and Shao, X. (2017). Martingale Difference Divergence Matrix and Its Application to Dimension Reduction for Stationary Multivariate Time Series. Journal of the American Statistical Association, 1-14. http://dx.doi.org/10.1080/01621459.2016.1240083.

Examples

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

mddm(X, Y, compute = "C")
mddm(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)

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