meantest {PEtests} | R Documentation |
Two-sample mean tests for high-dimensional data
Description
This function implements five two-sample mean tests on high-dimensional
mean vectors.
Let \mathbf{X} \in \mathbb{R}^p
and \mathbf{Y} \in \mathbb{R}^p
be two p
-dimensional populations with mean vectors
(\boldsymbol{\mu}_1, \boldsymbol{\mu}_2)
and covariance matrices
(\mathbf{\Sigma}_1, \mathbf{\Sigma}_2)
, respectively.
The problem of interest is to test the equality of the two
mean vectors of the two populations:
H_{0m}: \boldsymbol{\mu}_1 = \boldsymbol{\mu}_2.
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}
. We denote
dataX=
(\mathbf{X}_1, \ldots, \mathbf{X}_{n_1})^\top\in\mathbb{R}^{n_1\times p}
and dataY=
(\mathbf{Y}_1, \ldots, \mathbf{Y}_{n_2})^\top\in\mathbb{R}^{n_2\times p}
.
Usage
meantest(dataX,dataY,method='pe.comp',delta=NULL)
Arguments
dataX |
an |
dataY |
an |
method |
the method type (default =
|
delta |
This is needed only in |
Value
method
the method type
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.
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)
meantest(X,Y)