Description Usage Arguments Value References Examples
Computes the biascorrected estimator of the quadratic form of the regression vector, restricted to the set of indices G
for the high dimensional linear regression and the corresponding standard error.
It also constructs the confidence interval for the quadratic form and test whether it is above zero or not.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
X 
Design matrix, of dimension n x p 
y 
Outcome vector, of length n 
G 
The set of indices, 
Cov.weight 
Logical, if set to 
A 
The matrix A in the quadratic form, of dimension G\timesG (default = 
tau.vec 
The vector of enlargement factors for asymptotic variance of the biascorrected estimator to handle superefficiency (default = 1) 
init.coef 
Initial estimator for the regression vector (default = 
lambda 
The tuning parameter used in the construction of 
mu 
The dual tuning parameter used in the construction of the projection direction (default = 
step 
The step size used to compute 
resol 
Resolution or the factor by which 
maxiter 
Maximum number of steps along which 
alpha 
Level of significance to test the null hypothesis which claims that the quadratic form of the regression vector is equal to 0 (default = 0.05) 
verbose 
Should inetrmediate message(s) be printed (default = 
prop.est 
The biascorrected estimator of the quadratic form of the regression vector 
se 
The standard error of the biascorrected estimator 
CI 
The matrix of confidence interval for the quadratic form of the regression vector; row corresponds to different values of 
decision 

proj 
The projection direction, of length p 
plug.in 
The plugin estimator for the quadratic form of the regression vector restricted to 
grouplinSIHR
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  n = 100
p = 200
A1gen < function(rho,p){
A1=matrix(0,p,p)
for(i in 1:p){
for(j in 1:p){
A1[i,j]<rho^(abs(ij))
}
}
A1
}
mu < rep(0,p)
mu[1:5] < c(1:5)/5
rho = 0.5
Cov < (A1gen(rho,p))/2
beta < rep(0,p)
beta[1:10] < c(1:10)/5
X < MASS::mvrnorm(n,mu,Cov)
y = X%*%beta + rnorm(n)
test.set =c(30:50)
Est <SIHR::QF(X = X, y = y, G = test.set)

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