mdm_test {EDMeasure}R Documentation

Mutual Independence Tests

Description

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.

Usage

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 Rn\mathcal{R}_n based on distance covariance Vn\mathcal{V}_n;

  • sym_dcov: symmetric measure Sn\mathcal{S}_n based on distance covariance Vn\mathcal{V}_n;

  • comp: complete measure Qn\mathcal{Q}_n based on complete V-statistics;

  • comp_simp: simplified complete measure Qn\mathcal{Q}_n^\star based on incomplete V-statistics;

  • asym_comp: asymmetric measure Jn\mathcal{J}_n based on complete measure Qn\mathcal{Q}_n;

  • asym_comp_simp: simplified asymmetric measure Jn\mathcal{J}_n^\star based on simplified complete measure Qn\mathcal{Q}_n^\star;

  • sym_comp: symmetric measure In\mathcal{I}_n based on complete measure Qn\mathcal{Q}_n;

  • sym_comp_simp: simplified symmetric measure In\mathcal{I}_n^\star based on simplified complete measure Qn\mathcal{Q}_n^\star.

From experiments, asym_dcov, sym_dcov, comp_simp are recommended.

Value

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.

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.

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)

[Package EDMeasure version 1.2.0 Index]