cmdm_test function

Conditional Mean Independence Tests

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.

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.

Returns

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.

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)

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.