mdm_test function

Mutual Independence Tests

mdm_test tests mutual independence of all components in X, where each component contains one variable (univariate) or more variables (multivariate). All tests are implemented as permutation tests.

mdm_test(X, dim_comp = NULL, num_perm = NULL, type = "comp_simp")

Arguments

• X: A matrix or data frame, where rows represent samples, and columns represent variables.

• dim_comp: The numbers of variables contained by all components in X. If omitted, each component is assumed to contain exactly one variable.

• num_perm: The number of permutation samples drawn to approximate the asymptotic distributions of mutual dependence measures. If omitted, an adaptive number is used.

• type: The type of mutual dependence measures, including

  • asym_dcov: asymmetric measure $\mathcal{R}_n$ based on distance covariance $\mathcal{V}_n$;
  • sym_dcov: symmetric measure $\mathcal{S}_n$ based on distance covariance $\mathcal{V}_n$;
  • comp: complete measure $\mathcal{Q}_n$ based on complete V-statistics;
  • comp_simp: simplified complete measure $\mathcal{Q}_n^\star$ based on incomplete V-statistics;
  • asym_comp: asymmetric measure $\mathcal{J}_n$ based on complete measure $\mathcal{Q}_n$;
  • asym_comp_simp: simplified asymmetric measure $\mathcal{J}_n^\star$ based on simplified complete measure $\mathcal{Q}_n^\star$;
  • sym_comp: symmetric measure $\mathcal{I}_n$ based on complete measure $\mathcal{Q}_n$;
  • sym_comp_simp: simplified symmetric measure $\mathcal{I}_n^\star$ based on simplified complete measure $\mathcal{Q}_n^\star$.

  From experiments, asym_dcov, sym_dcov, comp_simp are recommended.

Returns

mdm_test returns a list including the following components: - stat: The value of the mutual dependence measure.

• pval: The p-value of the mutual independence test.

Examples

## Not run:

# X is a 10 x 3 matrix with 10 samples and 3 variables
X <- matrix(rnorm(10 * 3), 10, 3)

# assume X = (X1, X2) where X1 is 1-dim, X2 is 2-dim
mdm_test(X, dim_comp = c(1, 2), type = "asym_dcov")

# assume X = (X1, X2) where X1 is 2-dim, X2 is 1-dim
mdm_test(X, dim_comp = c(2, 1), type = "sym_dcov")

# assume X = (X1, X2, X3) where X1 is 1-dim, X2 is 1-dim, X3 is 1-dim
mdm_test(X, dim_comp = c(1, 1, 1), type = "comp_simp")
## End(Not run)

References

Jin, Z., and Matteson, D. S. (2017). Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence. arXiv preprint arXiv:1709.02532. https://arxiv.org/abs/1709.02532.