mutual independence | R Documentation |
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)
x |
data matrix or data frame |
R |
number of permutation replicates |
A population coefficient for mutual independence of d random variables, d ≥q 2, is
∑_{k=1}^{d-1} \mathcal R^2(X_k, [X_{k+1},…,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,…,X_d
the test statistic is the sum of the d-1 statistics (bias-corrected dcor^2 statistics):
∑_{k=1}^{d-1} \mathcal R_n^*(X_k, [X_{k+1},…,X_d])
.
mutualIndep.test
returns an object of class power.htest
.
See Szekely and Rizzo (2014) for details on unbiased dCov^2 and bias-corrected dCor^2 (bcdcor
) statistics.
Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely
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.
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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.