simultest.cauchy {PEtests} | R Documentation |
Two-sample simultaneous test using Cauchy combination
Description
This function implements the two-sample simultaneous test on high-dimensional
mean vectors and covariance matrices using Cauchy combination.
Suppose are i.i.d.
copies of
, and
are i.i.d. copies of
.
Let
and
denote the
-values associated with
the
-norm-based mean test proposed in Chen and Qin (2010)
(see
meantest.cq
for details)
and the -norm-based covariance test proposed in Li and Chen (2012)
(see
covtest.lc
for details),
respectively. The simultaneous test statistic via Cauchy combination is defined as
It has been proved that with some regularity conditions, under the null hypothesis
,
the two tests are asymptotically independent as
,
and therefore
asymptotically converges in distribution to
a standard Cauchy distribution.
The asymptotic
-value is obtained by
where is the cdf of the standard Cauchy distribution.
Usage
simultest.cauchy(dataX,dataY)
Arguments
dataX |
an |
dataY |
an |
Value
stat
the value of test statistic
pval
the p-value for the test.
References
Chen, S. X. and Qin, Y. L. (2010). A two-sample test for high-dimensional data with applications to gene-set testing. Annals of Statistics, 38(2):808–835.
Li, J. and Chen, S. X. (2012). Two sample tests for high-dimensional covariance matrices. The Annals of Statistics, 40(2):908–940.
Yu, X., Li, D., Xue, L., and Li, R. (2022). Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing. Journal of the American Statistical Association, (in press):1–14.
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)
simultest.cauchy(X,Y)