get_p_subGaussian {ISS}

get_p_subGaussian

Description

Calculate the p-value in Definition 1 of Müller et al. (2023).

Usage

get_p_subGaussian(X, y, x0, sigma2, tau)

Arguments

X

a numeric matrix specifying the covariates.

y

a numeric vector with length(y) == nrow(X) specifying the responses.

x0

a numeric vector specifying the point of interest, such that length(x0) == ncol(X).

sigma2

a single positive numeric value specifying the variance parameter.

tau

a single numeric value specifying the threshold of interest.

Value

A single numeric value in (0, 1].

References

Müller MM, Reeve HWJ, Cannings TI, Samworth RJ (2023). “Isotonic subgroup selection.” arXiv preprint arXiv:2305.04852.

Examples

set.seed(123)
n <- 100
d <- 2
X <- matrix(runif(d*n), ncol = d)
eta <- function(x) sum(x)
y <- apply(X, MARGIN = 1, FUN = eta) + rnorm(n, sd = 0.5)
get_p_subGaussian(X, y, x0 = c(1, 1), sigma2 = 0.25, tau = 1)
get_p_subGaussian(X, y, x0 = c(1, 1), sigma2 = 0.25, tau = 3)