indep.test {energy}  R Documentation 
Computes a multivariate nonparametric test of independence.
The default method implements the distance covariance test
dcov.test
.
indep.test(x, y, method = c("dcov","mvI"), index = 1, R)
x 
matrix: first sample, observations in rows 
y 
matrix: second sample, observations in rows 
method 
a character string giving the name of the test 
index 
exponent on Euclidean distances 
R 
number of replicates 
indep.test
with the default method = "dcov"
computes
the distance
covariance test of independence. index
is an exponent on
the Euclidean distances. Valid choices for index
are in (0,2],
with default value 1 (Euclidean distance). The arguments are passed
to the dcov.test
function. See the help topic dcov.test
for
the description and documentation and also see the references below.
indep.test
with method = "mvI"
computes the coefficient \mathcal I_n
and performs a nonparametric
\mathcal E
test of independence. The arguments are passed to
mvI.test
. The
index
argument is ignored (index = 1
is applied).
See the help topic mvI.test
and also
see the reference (2006) below for details.
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.
These energy tests of independence are based on related theoretical
results, but different test statistics.
The dcov
method is faster than mvI
method by
approximately a factor of O(n).
indep.test
returns a list with class
htest
containing
method 
description of test 
statistic 
observed value of the
test statistic 
estimate 

estimates 
a vector [dCov(x,y), dCor(x,y), dVar(x), dVar(y)] (method dcov) 
replicates 
replicates of the test statistic 
p.value 
approximate pvalue of the test 
data.name 
description of data 
As of energy1.10,
indep.etest
is deprecated and replaced by indep.test
, which
has methods for two different energy tests of independence. indep.test
applies
the distance covariance test (see dcov.test
) by default (method = "dcov"
).
The original indep.etest
applied the independence coefficient
\mathcal I_n
, which is now obtained by method = "mvI"
.
Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely
Szekely, G.J. and Rizzo, M.L. (2009),
Brownian Distance Covariance,
Annals of Applied Statistics, Vol. 3 No. 4, pp.
12361265. (Also see discussion and rejoinder.)
doi: 10.1214/09AOAS312
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. 27692794.
doi: 10.1214/009053607000000505
Bakirov, N.K., Rizzo, M.L., and Szekely, G.J. (2006), A Multivariate
Nonparametric Test of Independence, Journal of Multivariate Analysis
93/1, 5880,
doi: 10.1016/j.jmva.2005.10.005
## independent multivariate data
x < matrix(rnorm(60), nrow=20, ncol=3)
y < matrix(rnorm(40), nrow=20, ncol=2)
indep.test(x, y, method = "dcov", R = 99)
indep.test(x, y, method = "mvI", R = 99)
## dependent multivariate data
if (require(MASS)) {
Sigma < matrix(c(1, .1, 0, 0 , 1, 0, 0 ,.1, 1), 3, 3)
x < mvrnorm(30, c(0, 0, 0), diag(3))
y < mvrnorm(30, c(0, 0, 0), Sigma) * x
indep.test(x, y, R = 99) #dcov method
indep.test(x, y, method = "mvI", R = 99)
}