QF: Inference for quadratic forms of the regression vector in...

Description Usage Arguments Value References Examples

View source: R/QF.R

Description

Computes the bias-corrected 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.

Usage

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QF(
  X,
  y,
  G,
  Cov.weight = TRUE,
  A = NULL,
  tau.vec = c(1),
  init.coef = NULL,
  lambda = NULL,
  mu = NULL,
  step = NULL,
  resol = 1.5,
  maxiter = 6,
  alpha = 0.05,
  verbose = TRUE
)

Arguments

X

Design matrix, of dimension n x p

y

Outcome vector, of length n

G

The set of indices, G in the quadratic form

Cov.weight

Logical, if set to TRUE then A is the |G|\times|G| submatrix of the population covariance matrix corresponding to the index set G, else need to provide an A (default = TRUE)

A

The matrix A in the quadratic form, of dimension |G|\times|G| (default = NULL)

tau.vec

The vector of enlargement factors for asymptotic variance of the bias-corrected estimator to handle super-efficiency (default = 1)

init.coef

Initial estimator for the regression vector (default = NULL)

lambda

The tuning parameter used in the construction of init.coef (default = NULL)

mu

The dual tuning parameter used in the construction of the projection direction (default = NULL)

step

The step size used to compute mu; if set to NULL it is computed to be the number of steps (< maxiter) to obtain the smallest mu such that the dual optimization problem for constructing the projection direction converges (default = NULL)

resol

Resolution or the factor by which mu is increased/decreased to obtain the smallest mu such that the dual optimization problem for constructing the projection direction converges (default = 1.5)

maxiter

Maximum number of steps along which mu is increased/decreased to obtain the smallest mu such that the dual optimization problem for constructing the projection direction converges (default = 6)

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 = TRUE)

Value

prop.est

The bias-corrected estimator of the quadratic form of the regression vector

se

The standard error of the bias-corrected estimator

CI

The matrix of confidence interval for the quadratic form of the regression vector; row corresponds to different values of tau.vec

decision

decision=1 implies the quadratic form of the regression vector is above zero \newline decision=0 implies the quadratic form of the regression vector is zero \newline row corresponds to different values of tau.vec

proj

The projection direction, of length p

plug.in

The plug-in estimator for the quadratic form of the regression vector restricted to G

References

\insertRef

grouplinSIHR

Examples

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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(i-j))
 }
}
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)

SIHR documentation built on Oct. 7, 2021, 9:08 a.m.