meantest.pe.fisher {PEtests}R Documentation

Two-sample PE mean test for high-dimensional data via Fisher's combination

Description

This function implements the two-sample PE covariance test via Fisher's combination. Suppose {X1,,Xn1}\{\mathbf{X}_1, \ldots, \mathbf{X}_{n_1}\} are i.i.d. copies of X\mathbf{X}, and {Y1,,Yn2}\{\mathbf{Y}_1, \ldots, \mathbf{Y}_{n_2}\} are i.i.d. copies of Y\mathbf{Y}. Let pCQp_{CQ} and pCLXp_{CLX} denote the pp-values associated with the l2l_2-norm-based covariance test (see meantest.cq for details) and the ll_\infty-norm-based covariance test (see meantest.clx for details), respectively. The PE covariance test via Fisher's combination is defined as

MFisher=2log(pCQ)2log(pCLX).M_{Fisher} = -2\log(p_{CQ})-2\log(p_{CLX}).

It has been proved that with some regularity conditions, under the null hypothesis H0m:μ1=μ2,H_{0m}: \boldsymbol{\mu}_1 = \boldsymbol{\mu}_2, the two tests are asymptotically independent as n1,n2,pn_1, n_2, p\rightarrow \infty, and therefore MFisherM_{Fisher} asymptotically converges in distribution to a χ42\chi_4^2 distribution. The asymptotic pp-value is obtained by

p-value=1Fχ42(MFisher),p\text{-value} = 1-F_{\chi_4^2}(M_{Fisher}),

where Fχ42()F_{\chi_4^2}(\cdot) is the cdf of the χ42\chi_4^2 distribution.

Usage

meantest.pe.fisher(dataX,dataY)

Arguments

dataX

an n1n_1 by pp data matrix

dataY

an n2n_2 by pp data matrix

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.fisher(X,Y)

[Package PEtests version 0.1.0 Index]