tsbf_zwz2023 {HDNRA} | R Documentation |
Test proposed by Zhu et al. (2023)
Description
Zhu et al. (2023)'s test for testing equality of two-sample high-dimensional mean vectors without assuming that two covariance matrices are the same.
Usage
tsbf_zwz2023(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
Zhu et al. (2023) proposed the following test statistic:
where are the sample mean vectors and
is the estimator of
.
They showed that under the null hypothesis,
and an F-type mixture have the same normal or non-normal limiting distribution.
Value
A (list) object of S3
class htest
containing the following elements:
- p.value
the p-value of the test proposed by Zhu et al. (2023).
- statistic
the test statistic proposed by Zhu et al. (2023).
- df1
estimated approximate degrees of freedom
of Zhu et al. (2023)'s test.
- df2
estimated approximate degrees of freedom
of Zhu et al. (2023)'s test.
References
Zhu T, Wang P, Zhang J (2023). “Two-sample Behrens–Fisher problems for high-dimensional data: a normal reference F-type test.” Computational Statistics, 1–24. doi:10.1007/s00180-023-01433-6.
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_zwz2023(y1, y2)