Sim.CI {SILM}

Simultaneous Confidence Interval

Description

This function implements the method for constructing simultaneous confidence interval in Zhang and Cheng (2017).

Usage

Sim.CI(X, Y, set, M = 500, alpha = 0.95)

Arguments

X

n times p design matrix.

Y

Response variable.

set

The set of variables of interest.

M

The number of bootstrap replications (default 500).

alpha

The nominal level alpha (default 0.95).

Value

The de-biased Lasso estimator, the confidence bands (lower bound and upper bound) delivered by the non-studentized and the studentized statistics.

References

Zhang, X., and Cheng, G. (2017) Simultaneous Inference for High-dimensional Linear Models, Journal of the American Statistical Association, 112, 757-768.

Examples

## The function is intended for large n and p.
## Use small p here for illustration purpose only.
n <- 100
p <- 10
s0 <- 3
set <- 1:s0
Sigma <- matrix(NA, p, p)
for (i in 1:p) Sigma[i,] <- 0.9^(abs(i-(1:p)))
X <- matrix(rnorm(n*p), n, p)
X <- t(t(chol(Sigma))%*%t(X))
beta <- rep(0,p)
beta[1:s0] <- runif(s0,0,2)
Y <- X%*%beta+rt(n,4)/sqrt(2)
Sim.CI(X, Y, set)