glht_fhw2004 {HDNRA} | R Documentation |
Test proposed by Fujikoshi et al. (2004)
Description
Fujikoshi et al. (2004)'s test for general linear hypothesis testing (GLHT) problem for high-dimensional data with assuming that underlying covariance matrices are the same.
Usage
glht_fhw2004(Y,X,C)
Arguments
Y |
An |
X |
A known |
C |
A known matrix of size |
Details
A high-dimensional linear regression model can be expressed as
where is a
unknown parameter matrix and
is an
error matrix.
It is of interest to test the following GLHT problem
Fujikoshi et al. (2004) proposed the following test statistic:
where and
are the matrices of sums of squares and products due to the hypothesis and the error, respecitively.
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 Fujikoshi et al. (2004).
- p.value
the
-value of the test proposed by Fujikoshi et al. (2004).
References
Fujikoshi Y, Himeno T, Wakaki H (2004). “Asymptotic results of a high dimensional MANOVA test and power comparison when the dimension is large compared to the sample size.” Journal of the Japan Statistical Society, 34(1), 19–26. doi:10.14490/jjss.34.19.
Examples
set.seed(1234)
k <- 3
q <- k-1
p <- 50
n <- c(25,30,40)
rho <- 0.01
Theta <- matrix(rep(0,k*p),nrow=k)
X <- matrix(c(rep(1,n[1]),rep(0,sum(n)),rep(1,n[2]),rep(0,sum(n)),rep(1,n[3])),ncol=k,nrow=sum(n))
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)
U <- matrix(ncol = sum(n),nrow=p)
for(i in 1:sum(n)){
U[,i] <- rnorm(p,0,1)
}
Y <- X%*%Theta+t(U)%*%Gamma
C <- cbind(diag(q),-rep(1,q))
glht_fhw2004(Y,X,C)