meantest.clx {PEtests}

Two-sample high-dimensional mean test (Cai, Liu and Xia, 2014)

Description

This function implements the two-sample l_\infty-norm-based high-dimensional mean test proposed in Cai, Liu and Xia (2014). 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}. The test statistic is defined as

M_{CLX}=\frac{n_1n_2}{n_1+n_2}\max_{1\leq j\leq p} \frac{(\bar{X_j}-\bar{Y_j})^2} {\frac{1}{n_1+n_2} [\sum_{u=1}^{n_1} (X_{uj}-\bar{X_j})^2+\sum_{v=1}^{n_2} (Y_{vj}-\bar{Y_j})^2] }

With some regularity conditions, under the null hypothesis H_{0c}: \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2, the test statistic M_{CLX}-2\log p+\log\log p converges in distribution to a Gumbel distribution G_{mean}(x) = \exp(-\frac{1}{\sqrt{\pi}}\exp(-\frac{x}{2})) as n_1, n_2, p \rightarrow \infty. The asymptotic p-value is obtained by

p_{CLX} = 1-G_{mean}(M_{CLX}-2\log p+\log\log p).

Usage

meantest.clx(dataX,dataY)

Arguments

dataX

an n_1 by p data matrix

dataY

an n_2 by p data matrix

Value

stat the value of test statistic

pval the p-value for the test.

References

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.clx(X,Y)