Description Usage Arguments Details Value Note Author(s) References See Also
Computes the multivariate nonparametric E-statistic and test of independence based on independence coefficient I_n.
1 2 |
x |
matrix: first sample, observations in rows |
y |
matrix: second sample, observations in rows |
R |
number of replicates |
Computes the coefficient I_n and performs a nonparametric
E-test of independence. 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. The statistic
E = I^2 is a ratio of V-statistics based
on interpoint distances ||x_{i}-y_{j}||.
See the reference below for details.
mvI
returns the statistic. mvI.test
returns
a list with class
htest
containing
method |
description of test |
statistic |
observed value of the test statistic n I_n^2 |
estimate |
I_n |
replicates |
replicates of the test statistic |
p.value |
approximate p-value of the test |
data.name |
description of data |
Historically this is the first energy test of independence. The
distance covariance test dcov.test
, distance correlation
dcor
, and related methods are more recent (2007,2009).
The distance covariance test is faster and has different properties than
mvI.test
. Both methods are based on a population independence coefficient
that characterizes independence and both tests are statistically consistent.
Maria L. Rizzo mrizzo @ bgsu.edu and Gabor J. Szekely
Bakirov, N.K., Rizzo, M.L., and Szekely, G.J. (2006), A Multivariate
Nonparametric Test of Independence, Journal of Multivariate Analysis
93/1, 58-80,
http://dx.doi.org/10.1016/j.jmva.2005.10.005
indep.test
mvI.test
dcov.test
dcov
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