covtest.lc {PEtests} | R Documentation |
Two-sample high-dimensional covariance test (Li and Chen, 2012)
Description
This function implements the two-sample -norm-based high-dimensional covariance test
proposed by Li and Chen (2012).
Suppose
are i.i.d.
copies of
, and
are i.i.d. copies of
. The test statistic
is
defined as
where ,
, and
are unbiased estimators for
,
,
and
, respectively.
Under the null hypothesis
,
the leading variance of
is
,
which can be consistently estimated by
.
The explicit formulas of
,
,
and
can be found in
Equations (2.1), (2.2) and Theorem 1 of Li and Chen (2012).
With some regularity conditions, under the null hypothesis
,
the test statistic
converges in distribution to a standard normal distribution
as
.
The asymptotic
-value is obtained by
where is the cdf of the standard normal distribution.
Usage
covtest.lc(dataX,dataY)
Arguments
dataX |
an |
dataY |
an |
Value
stat
the value of test statistic
pval
the p-value for the test.
References
Li, J. and Chen, S. X. (2012). Two sample tests for high-dimensional covariance matrices. The Annals of Statistics, 40(2):908–940.
Examples
n1 = 100; n2 = 100; pp = 500
set.seed(1)
X = matrix(rnorm(n1*pp), nrow=n1, ncol=pp)
Y = matrix(rnorm(n2*pp), nrow=n2, ncol=pp)
covtest.lc(X,Y)