Computes the multivariate nonparametric E-statistic and test of independence
based on independence coefficient I_n.
Usage
mvI.test(x, y, R=199)
mvI(x, y)
Arguments
x
matrix: first sample, observations in rows
y
matrix: second sample, observations in rows
R
number of replicates
Details
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.
Value
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
Note
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.
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