Step {SILM}

Stepdown Method for Multiple Testing

Description

This function implements the stepdown method in Zhang and Cheng (2017).

Usage

Step(X, Y, M = 500, alpha = 0.05)

Arguments

X

n times p design matrix.

Y

Response variable.

M

The number of bootstrap replications (default 500).

alpha

The nominal level alpha (default 0.05).

Value

A vector indicating which hypotheses are being rejected.

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(s0,1,2)
Y <- X%*%beta+rt(n,4)/sqrt(2)
Step(X, Y, M=500, alpha=0.05)