cmdm_test {EDMeasure}

Conditional Mean Independence Tests

Description

cmdm_test tests conditional mean independence of Y given X conditioning on Z, where each contains one variable (univariate) or more variables (multivariate). All tests are implemented as permutation tests.

Usage

cmdm_test(X, Y, Z, num_perm = 500, type = "linmdd", 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.

Z

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

num_perm

The number of permutation samples drawn to approximate the asymptotic distributions of mutual dependence measures.

type

The type of conditional mean dependence measures, including

• linmdd: martingale difference divergence under a linear assumption;

• pmdd: partial martingale difference divergence.

compute

The computation method for martingale difference divergence, including

• C: computation implemented in C code;

• R: computation implemented in R code.

center

The centering approach for martingale difference divergence, including

• U: U-centering which leads to an unbiased estimator;

• D: double-centering which leads to a biased estimator.

Value

cmdm_test returns a list including the following components:

stat

The value of the conditional mean dependence measure.

dist

The p-value of the conditional mean independence test.

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.

Examples

## Not run: 
# X, Y, Z are vectors with 10 samples and 1 variable
X <- rnorm(10)
Y <- rnorm(10)
Z <- rnorm(10)

cmdm_test(X, Y, Z, type = "linmdd")

# 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)

cmdm_test(X, Y, Z, type = "pmdd")

## End(Not run)