mutualIndep: Energy Test of Mutual Independence

In energy: E-Statistics: Multivariate Inference via the Energy of Data

Energy Test of Mutual Independence

Description

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.

Usage

mutualIndep.test(x, R)

Arguments

x	data matrix or data frame
R	number of permutation replicates

Details

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])

.

Value

mutualIndep.test returns an object of class power.htest.

Note

See Szekely and Rizzo (2014) for details on unbiased dCov^2 and bias-corrected dCor^2 (bcdcor) statistics.

Author(s)

Maria L. Rizzo [e-mail] and Gabor J. Szekely

References

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.
\Sexpr[results=rd]{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.

See Also

bcdcor, dcovU_stats

Examples

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

energy documentation built on Sept. 11, 2024, 7:57 p.m.