ks_s2007 {HDNRA} | R Documentation |
Test proposed by Schott (2007)
Description
Schott, J. R. (2007)'s test for one-way MANOVA problem for high-dimensional data with assuming that underlying covariance matrices are the same.
Usage
ks_s2007(Y,n,p)
Arguments
Y |
A list of |
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 one-way MANOVA problem:
Schott (2007) proposed the following test statistic:
where ,
,
, and
, with
.
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 Schott (2007).
- p.value
the
-value of the test proposed by Schott (2007).
References
Schott JR (2007). “Some high-dimensional tests for a one-way MANOVA.” Journal of Multivariate Analysis, 98(9), 1825–1839. doi:10.1016/j.jmva.2006.11.007.
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]))
}
ks_s2007(Y, n, p)