meantest.pe.cauchy {PEtests} | R Documentation |
Two-sample PE mean test for high-dimensional data via Cauchy combination
Description
This function implements the two-sample PE covariance test via
Cauchy combination.
Suppose \{\mathbf{X}_1, \ldots, \mathbf{X}_{n_1}\}
are i.i.d.
copies of \mathbf{X}
, and \{\mathbf{Y}_1, \ldots, \mathbf{Y}_{n_2}\}
are i.i.d. copies of \mathbf{Y}
.
Let p_{CQ}
and p_{CLX}
denote the p
-values associated with
the l_2
-norm-based covariance test (see meantest.cq
for details)
and the l_\infty
-norm-based covariance test
(see meantest.clx
for details), respectively.
The PE covariance test via Cauchy combination is defined as
M_{Cauchy} = \frac{1}{2}\tan((0.5-p_{CQ})\pi) + \frac{1}{2}\tan((0.5-p_{CLX})\pi).
It has been proved that with some regularity conditions, under the null hypothesis
H_{0m}: \boldsymbol{\mu}_1 = \boldsymbol{\mu}_2,
the two tests are asymptotically independent as n_1, n_2, p\rightarrow \infty
,
and therefore M_{Cauchy}
asymptotically converges in distribution to a standard Cauchy distribution.
The asymptotic p
-value is obtained by
p\text{-value} = 1-F_{Cauchy}(M_{Cauchy}),
where F_{Cauchy}(\cdot)
is the cdf of the standard Cauchy distribution.
Usage
meantest.pe.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.
Cai, T. T., Liu, W., and Xia, Y. (2014). Two-sample test of high dimensional means under dependence. Journal of the Royal Statistical Society: Series B: Statistical Methodology, 76(2):349–372.
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)
meantest.pe.cauchy(X,Y)