Calculates the block-multiplier bootstrap test.

This function test \(H_{0,j}: Y_j \perp X\), for \(j=1,\dots,p\) using the block-multiplier bootstrap test of Olivares, Olma, and Wilhelm (2025).

Usage

BMB_indep(dat, B, alpha, type = "bmb1", seed = NULL)

Arguments

dat: Data frame. There are two elements in the data frame, X and Y, where X is a random variable and Y corresponds with the \(Y_j\) in the individual hypothesis \(Y_j \perp X\).
B: Numeric. The number of bootstrap samples.
alpha: Numeric. The significance level.
type: Character. This argument specifies whether and how the test statistic and the bootstrap statistic are studentized. Options are "bmb" (no studentization), "bmb1" (default option), and "bmb2" (alternative studentization). The types are formally described in Olivares, Olma, and Wilhelm (2025).
seed: Numeric. The seed for the random number generator. If NULL, the seed is not set. If a positive integer, it sets the seed for reproducibility.

Value

An object of class "BMB_indep", a list containing the following components:

type: Type. See description above
T_obs: The value of the test statistic.
n: Sample Size.
p: Number of hypotheses.
block_size: Block size used in the bootstrap.
B: Number of bootstrap samples.
cv: Bootstrap critical value corresponding to the test statistic.

References

Olivares, M., Olma, T., and Wilhelm, D. (2025). A Powerful Bootstrap Test of Independence in High Dimensions. Preprint, arXiv:2503.21715.

Author

Maurcio Olivares

Tomasz Olma

Daniel Wilhelm

Examples

if (FALSE) { # \dontrun{
n <- 100
p <- 10
dat <- list()
dat$X <- rnorm(n)
dat$Y <- MASS::mvrnorm(n = n, mu = rep(0,  p), Sigma=diag(rep(1, p)))
test_indep <- BMB_indep(dat, B=100, alpha=0.05, type = "bmb", seed = 5)
summary(test_indep)

} # }