ts_sd2008 {HDNRA} | R Documentation |
Test proposed by Srivastava and Du (2008)
Description
Srivastava and Du (2008)'s test for testing equality of two-sample high-dimensional mean vectors with assuming that two covariance matrices are the same.
Usage
ts_sd2008(y1, y2)
Arguments
y1 |
The data matrix (p by n1) from the first population. Each column represents a |
y2 |
The data matrix (p by n2) from the first population. Each column represents a |
Details
Suppose we have two independent high-dimensional samples:
The primary object is to test
Srivastava and Du (2008) proposed the following test statistic:
where are the sample mean vectors,
is the diagonal matrix of sample variance,
is the sample correlation matrix and
is the adjustment coefficient proposed by Srivastava and Du (2008).
They showed that under the null hypothesis,
is asymptotically normally distributed.
Value
A (list) object of S3
class htest
containing the following elements:
- statistic
the test statistic proposed by Srivastava and Du (2008).
- p.value
the
-value of the test proposed by Srivastava and Du (2008).
- cpn
the adjustment coefficient proposed by Srivastava and Du (2008).
References
Srivastava MS, Du M (2008). “A test for the mean vector with fewer observations than the dimension.” Journal of Multivariate Analysis, 99(3), 386–402. doi:10.1016/j.jmva.2006.11.002.
Examples
set.seed(1234)
n1 <- 20
n2 <- 30
p <- 50
mu1 <- t(t(rep(0, p)))
mu2 <- mu1
rho <- 0.1
y <- (-2 * sqrt(1 - rho) + sqrt(4 * (1 - rho) + 4 * p * rho)) / (2 * p)
x <- y + sqrt((1 - rho))
Gamma <- matrix(rep(y, p * p), nrow = p)
diag(Gamma) <- rep(x, p)
Z1 <- matrix(rnorm(n1 * p, mean = 0, sd = 1), p, n1)
Z2 <- matrix(rnorm(n2 * p, mean = 0, sd = 1), p, n2)
y1 <- Gamma %*% Z1 + mu1 %*% (rep(1, n1))
y2 <- Gamma %*% Z2 + mu2 %*% (rep(1, n2))
ts_sd2008(y1, y2)