glht_zz2022 {HDNRA} | R Documentation |
Test proposed by Zhu and Zhang (2022)
Description
Zhu and Zhang (2022)'s test for general linear hypothesis testing (GLHT) problem for high-dimensional data with assuming that underlying covariance matrices are the same.
Usage
glht_zz2022(Y,G,n,p)
Arguments
Y |
A list of |
G |
A known full-rank coefficient matrix ( |
n |
A vector of |
p |
The dimension of data. |
Details
Suppose we have the following independent high-dimensional samples:
It is of interest to test the following GLHT problem:
where
is a
matrix collecting
mean vectors and
is a known full-rank coefficient matrix with
.
Zhu and Zhang (2022) proposed the following test statistic:
where , and
, with
being the sample mean vectors and
being the usual pooled sample covariance matrix of the
samples.
They showed that under the null hypothesis, and a chi-squared-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
-value of the test proposed by Zhu and Zhang (2022).
- statistic
the test statistic proposed by Zhu and Zhang (2022).
- beta0
the parameter used in Zhu and Zhang (2022)'s test.
- beta1
the parameter used in Zhu and Zhang (2022)'s test.
- df
estimated approximate degrees of freedom of Zhu and Zhang (2022)'s test.
References
Zhu T, Zhang J (2022). “Linear hypothesis testing in high-dimensional one-way MANOVA: a new normal reference approach.” Computational Statistics, 37(1), 1–27. doi:10.1007/s00180-021-01110-6.
Examples
set.seed(1234)
k <- 3
p <- 50
n <- c(25, 30, 40)
rho <- 0.1
M <- matrix(rep(0, k * p), nrow = k, ncol = p)
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)
Y <- list()
for (g in 1:k) {
Z <- matrix(rnorm(n[g] * p, mean = 0, sd = 1), p, n[g])
Y[[g]] <- Gamma %*% Z + t(t(M[g, ])) %*% (rep(1, n[g]))
}
G <- cbind(diag(k - 1), rep(-1, k - 1))
glht_zz2022(Y, G, n, p)