apval_Sri2008 {highmean} | R Documentation |
Asymptotics-Based p-value of the Test Proposed by Srivastava and Du (2008)
Description
Calculates p-value of the test for testing equality of two-sample high-dimensional mean vectors proposed by Srivastava and Du (2008) based on the asymptotic distribution of the test statistic.
Usage
apval_Sri2008(sam1, sam2)
Arguments
sam1 |
an n1 by p matrix from sample population 1. Each row represents a |
sam2 |
an n2 by p matrix from sample population 2. Each row represents a |
Details
Suppose that the two groups of -dimensional independent and identically distributed samples
and
are observed; we consider high-dimensional data with
. Assume that the two groups share a common covariance matrix. The primary object is to test
versus
. Let
be the sample mean for group
. Also, let
be the pooled sample covariance matrix from the two groups.
Srivastava and Du (2008) proposed the following test statistic:
where ,
's are the diagonal elements of
,
is the sample correlation matrix and
. This test statistic follows normal distribution under the null hypothesis.
Value
A list including the following elements:
sam.info |
the basic information about the two groups of samples, including the samples sizes and dimension. |
cov.assumption |
this output reminds users that the two sample populations have a common covariance matrix. |
method |
this output reminds users that the p-values are obtained using the asymptotic distributions of test statistics. |
pval |
the p-value of the test proposed by Srivastava and Du (2008). |
Note
The asymptotic distribution of the test statistic was derived under normality assumption in Bai and Saranadasa (1996). Also, this function assumes that the two sample populations have a common covariance matrix.
References
Srivastava MS and Du M (2008). "A test for the mean vector with fewer observations than the dimension." Journal of Multivariate Analysis, 99(3), 386–402.
See Also
Examples
library(MASS)
set.seed(1234)
n1 <- n2 <- 50
p <- 200
mu1 <- rep(0, p)
mu2 <- mu1
mu2[1:10] <- 0.2
true.cov <- 0.4^(abs(outer(1:p, 1:p, "-"))) # AR1 covariance
sam1 <- mvrnorm(n = n1, mu = mu1, Sigma = true.cov)
sam2 <- mvrnorm(n = n2, mu = mu2, Sigma = true.cov)
apval_Sri2008(sam1, sam2)