MDCcure (version 0.1.0)

mdd: Martingale Difference Divergence (MDD)

Description

mdd computes the squared martingale difference divergence (MDD) between response variable(s) Y and explanatory variable(s) X, measuring conditional mean dependence.

Usage

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

Value

Returns the squared Martingale Difference Divergence of Y given X.

Arguments

X

A vector or matrix where rows represent samples and columns represent variables.

Y

A vector or matrix where rows represent samples and columns represent variables.

center

Character string indicating the centering method to use. One of:

• "U": U-centering, which provides an unbiased estimator.

• "D": Double-centering, which leads to a biased estimator.

Default is "U".

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. tools:::Rd_expr_doi("10.1080/01621459.2014.887012").

Examples

# Generate example data
set.seed(123)
n <- 50
x <- matrix(rnorm(n * 5), nrow = n)  # multivariate explanatory variables
y_vec <- rbinom(n, 1, 0.5)           # univariate response
y_mat <- matrix(rnorm(n * 2), nrow = n)  # multivariate response

# Compute MDD with vector Y and U-centering
mdd(x, y_vec, center = "U")

# Compute MDD with matrix Y and double-centering
mdd(x, y_mat, center = "D")