tsbf_skk2013 {HDNRA} | R Documentation |
Test proposed by Srivastava et al. (2013)
Description
Srivastava et al. (2013)'s test for testing equality of two-sample high-dimensional mean vectors without assuming that two covariance matrices are the same.
Usage
tsbf_skk2013(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 et al. (2013) proposed the following test statistic:
where are the sample mean vectors,
with
being the diagonal matrices consisting of only the diagonal elements of the sample covariance matrices.
is given by equation (1.18) in Srivastava et al. (2013), and
is the adjustment coefficient proposed by Srivastava et al. (2013).
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 et al. (2013)
- p.value
the
-value of the test proposed by Srivastava et al. (2013)
- cpn
the adjustment coefficient proposed by Srivastava et al. (2013)
References
Srivastava MS, Katayama S, Kano Y (2013). “A two sample test in high dimensional data.” Journal of Multivariate Analysis, 114, 349–358. doi:10.1016/j.jmva.2012.08.014.
Examples
set.seed(1234)
n1 <- 20
n2 <- 30
p <- 50
mu1 <- t(t(rep(0, p)))
mu2 <- mu1
rho1 <- 0.1
rho2 <- 0.2
a1 <- 1
a2 <- 2
w1 <- (-2 * sqrt(a1 * (1 - rho1)) + sqrt(4 * a1 * (1 - rho1) + 4 * p * a1 * rho1)) / (2 * p)
x1 <- w1 + sqrt(a1 * (1 - rho1))
Gamma1 <- matrix(rep(w1, p * p), nrow = p)
diag(Gamma1) <- rep(x1, p)
w2 <- (-2 * sqrt(a2 * (1 - rho2)) + sqrt(4 * a2 * (1 - rho2) + 4 * p * a2 * rho2)) / (2 * p)
x2 <- w2 + sqrt(a2 * (1 - rho2))
Gamma2 <- matrix(rep(w2, p * p), nrow = p)
diag(Gamma2) <- rep(x2, p)
Z1 <- matrix(rnorm(n1*p,mean = 0,sd = 1), p, n1)
Z2 <- matrix(rnorm(n2*p,mean = 0,sd = 1), p, n2)
y1 <- Gamma1 %*% Z1 + mu1%*%(rep(1,n1))
y2 <- Gamma2 %*% Z2 + mu2%*%(rep(1,n2))
tsbf_skk2013(y1, y2)