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.
data matrix or data frame
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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