mdm {EDMeasure} R Documentation

## Mutual Dependence Measures

### Description

mdm measures mutual dependence of all components in X, where each component contains one variable (univariate) or more variables (multivariate).

### Usage

mdm(X, dim_comp = NULL, dist_comp = FALSE, 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. dist_comp Logical. If TRUE, the distances between all components from all samples in X will be returned. 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.

### Value

mdm returns a list including the following components:

 stat The value of the mutual dependence measure. dist The distances between all components from all samples.

### 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

# 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(X, dim_comp = c(1, 2), type = "asym_dcov")

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


[Package EDMeasure version 1.2.0 Index]