bootstrap.SEPaLS {SEPaLS}

Bootstrap function for SEPaLS estimator.

Description

Bootstrap function for SEPaLS estimator.

Usage

bootstrap.SEPaLS(
  X,
  Y,
  yn,
  type = c("vMF", "Laplace"),
  mu0 = NULL,
  kappa0 = NULL,
  lambda = NULL,
  B = 20
)

Arguments

X

(n\times p)-dimensional matrix of the covariates.

Y

(n)-dimensional vector of the response.

yn

y_n the quantile corresponding to lowest values of Ys to put in the tail.

type

character, whether vMF for von Mises-Fisher prior or Laplace for Laplace prior. See details.

mu0

\mu_0, unitary (p)-dimensional vector. The direction parameter for the vMF prior.

kappa0

\kappa_0, positive. The concentration parameter for the vMF prior.

lambda

\lambda, positive. The concentration parameter for the Laplace prior.

B

positive integer. The number of bootstrap samples on which estimate the SEPaLS directions. Default to 20.

Value

A list with two elements:

• ws: A (B\times p)-dimensional matrix with each row corresponding to the SEPaLS direction estimated on each bootstrap sample.

• cor: The correlation of each estimate direction on the Out-Of-Bag (OOB) sample with the response.

See Also

SEPaLS

Examples

set.seed(5)
n <- 3000
p <- 10
X <- matrix(rnorm(n*p),n,p)
beta <- c(5:1,rep(0,p-5)) ; beta <- beta/sqrt(sum(beta^2))
Y <- (X%*%beta)^3 + rnorm(n)
boot.sepals_Laplace <- bootstrap.SEPaLS(X,Y,yn=1,type="Laplace",lambda=0.01,
B=100)
boxplot(boot.sepals_Laplace$ws);abline(h=0,col="red",lty=2)