The test statistic is the sum of d-1 bias-corrected squared dcor statistics where the number of variables is d. Implementation is by permuation test.

`mutualIndep.test(x, R)`

`mutualIndep.test`

returns an object of class `power.htest`

.

- x
data matrix or data frame

- R
number of permutation replicates

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

A population coefficient for mutual independence of d random variables, \(d \geq 2\), is $$ \sum_{k=1}^{d-1} \mathcal R^2(X_k, [X_{k+1},\dots,X_d]). $$ which is non-negative and equals zero iff mutual independence holds. For example, if d=4 the population coefficient is $$ \mathcal R^2(X_1, [X_2,X_3,X_4]) + \mathcal R^2(X_2, [X_3,X_4]) + \mathcal R^2(X_3, X_4), $$ A permutation test is implemented based on the corresponding sample coefficient. To test mutual independence of $$X_1,\dots,X_d$$ the test statistic is the sum of the d-1 statistics (bias-corrected \(dcor^2\) statistics): $$\sum_{k=1}^{d-1} \mathcal R_n^*(X_k, [X_{k+1},\dots,X_d])$$.

Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007),
Measuring and Testing Dependence by Correlation of Distances,
*Annals of Statistics*, Vol. 35 No. 6, pp. 2769-2794.

tools:::Rd_expr_doi("10.1214/009053607000000505")

Szekely, G.J. and Rizzo, M.L. (2014),
Partial Distance Correlation with Methods for Dissimilarities.
*Annals of Statistics*, Vol. 42 No. 6, 2382-2412.

`bcdcor`

, `dcovU_stats`

```
x <- matrix(rnorm(100), nrow=20, ncol=5)
mutualIndep.test(x, 199)
```

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