glht_sf2006 {HDNRA} | R Documentation |
Test proposed by Srivastava and Fujikoshi (2006)
Description
Srivastava and Fujikoshi (2006)'s test for general linear hypothesis testing (GLHT) problem for high-dimensional data with assuming that underlying covariance matrices are the same.
Usage
glht_sf2006(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
Srivastava and Fujikoshi (2006) proposed the following test statistic:
where and
are the matrix of sum of squares and products due to error and the error, respectively, and
.
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 and Fujikoshi (2006).
- p.value
the
-value of the test proposed by Srivastava and Fujikoshi (2006).
References
Srivastava MS, Fujikoshi Y (2006). “Multivariate analysis of variance with fewer observations than the dimension.” Journal of Multivariate Analysis, 97(9), 1927–1940. doi:10.1016/j.jmva.2005.08.010.
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_sf2006(Y,X,C)