EDMeasure-package {EDMeasure} | R Documentation |

EDMeasure: A package for energy-based dependence measures

The EDMeasure package provides measures of mutual dependence and tests of mutual independence, independent component analysis methods based on mutual dependence measures, and measures of conditional mean dependence and tests of conditional mean independence.

The three main parts are:

mutual dependence measures via energy statistics

measuring mutual dependence

testing mutual independence

independent component analysis via mutual dependence measures

applying mutual dependence measures

initializing local optimization methods

conditional mean dependence measures via energy statistics

measuring conditional mean dependence

testing conditional mean independence

**Measuring mutual dependence**

The mutual dependence measures include:

asymmetric measure

`\mathcal{R}_n`

based on distance covariance`\mathcal{V}_n`

symmetric measure

`\mathcal{S}_n`

based on distance covariance`\mathcal{V}_n`

complete measure

`\mathcal{Q}_n`

based on complete V-statisticssimplified complete measure

`\mathcal{Q}_n^\star`

based on incomplete V-statisticsasymmetric measure

`\mathcal{J}_n`

based on complete measure`\mathcal{Q}_n`

simplified asymmetric measure

`\mathcal{J}_n^\star`

based on simplified complete measure`\mathcal{Q}_n^\star`

symmetric measure

`\mathcal{I}_n`

based on complete measure`\mathcal{Q}_n`

simplified symmetric measure

`\mathcal{I}_n^\star`

based on simplified complete measure`\mathcal{Q}_n^\star`

**Testing mutual independence**

The mutual independence tests based on the mutual dependence measures are implemented as permutation tests.

**Applying mutual dependence measures**

The mutual dependence measures include:

distance-based energy statistics

asymmetric measure

`\mathcal{R}_n`

based on distance covariance`\mathcal{V}_n`

symmetric measure

`\mathcal{S}_n`

based on distance covariance`\mathcal{V}_n`

simplified complete measure

`\mathcal{Q}_n^\star`

based on incomplete V-statistics

kernel-based maximum mean discrepancies

d-variable Hilbert–Schmidt independence criterion dHSIC

`_n`

based on Hilbert–Schmidt independence criterion HSIC`_n`

**Initializing local optimization methods**

The initialization methods include:

Latin hypercube sampling

Bayesian optimization

**Measuring conditional mean dependence**

The conditional mean dependence measures include:

conditional mean dependence of

`Y`

given`X`

martingale difference divergence

martingale difference correlation

martingale difference divergence matrix

conditional mean dependence of

`Y`

given`X`

adjusting for the dependence on`Z`

partial martingale difference divergence

partial martingale difference correlation

**Testing conditional mean independence**

The conditional mean independence tests include:

conditional mean independence of

`Y`

given`X`

conditioning on`Z`

martingale difference divergence under a linear assumption

partial martingale difference divergence

The conditional mean independence tests based on the conditional mean dependence measures are implemented as permutation tests.

Ze Jin zj58@cornell.edu,
Shun Yao shunyao2@illinois.edu,

David S. Matteson matteson@cornell.edu,
Xiaofeng Shao xshao@illinois.edu

[Package *EDMeasure* version 1.2.0 Index]