R: Energy Statistic Test of Independence

mvI.test {energy} | R Documentation

## Energy Statistic Test of Independence

### Description

Computes the multivariate nonparametric E-statistic and test of independence based on independence coefficient I_n.

### Usage

        mvI.test(x, y, R)
        mvI(x, y)

### Arguments

`x` | matrix: first sample, observations in rows
`y` | matrix: second sample, observations in rows
`R` | number of replicates

### Details

Computes the coefficient I_n and performs a nonparametric E-test of independence. The test decision is obtained via bootstrap, with `R` replicates. The sample sizes (number of rows) of the two samples must agree, and samples must not contain missing values. The statistic E = I^2 is a ratio of V-statistics based on interpoint distances ||x_{i}-y_{j}||. See the reference below for details.

### Value

`mvI` returns the statistic. `mvI.test` returns a list with class `htest` containing

`method` | description of test
`statistic` | observed value of the test statistic n I_n^2
`estimate` | I_n
`replicates` | replicates of the test statistic
`p.value` | approximate p-value of the test
`data.name` | description of data

### Note

Historically this is the first energy test of independence. The distance covariance test `dcov.test`, distance correlation `dcor`, and related methods are more recent (2007,2009). The distance covariance test is faster and has different properties than `mvI.test`. Both methods are based on a population independence coefficient that characterizes independence and both tests are statistically consistent.

### Author(s)

Maria L. Rizzo mrizzo @ bgsu.edu and Gabor J. Szekely

### References

Bakirov, N.K., Rizzo, M.L., and Szekely, G.J. (2006), A Multivariate Nonparametric Test of Independence, Journal of Multivariate Analysis 93/1, 58-80,
http://dx.doi.org/10.1016/j.jmva.2005.10.005

### See Also

`indep.test` `mvI.test` `dcov.test` `dcov`

[Package energy version 1.7-6 Index]