get_p_value {ISS}

get_p_value

Description

A wrapper function used to call the correct function for calculating the p-value.

Usage

get_p_value(
  p_value_method = c("sub-Gaussian-normalmixture", "sub-Gaussian", "Gaussian",
    "classification", "quantile"),
  X,
  y,
  x0,
  tau,
  sigma2,
  rho = 1/2,
  theta = 1/2
)

Arguments

p_value_method

one of c("sub-Gaussian", "sub-Gaussian-normalmixture", "Gaussian", "classification", "quantile") specifying which p-value construction should be used. See Definitions 1, 18, 19 and 21 and Lemma 24 by Müller et al. (2023) respectively. For p_value_method == "quantile", the version with the p-value from Definition 19 is implemented.

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).

tau

a single numeric value specifying the threshold of interest.

sigma2

a single positive numeric value specifying the variance parameter (required only if p_value_method %in% c("sub-Gaussian", "sub-Gaussian-normalmixture").

rho

a single positive numeric value serving as hyperparameter (required only if p_value_method == "sub-Gaussian-normalmixture").

theta

a single numeric value in (0, 1) specifying the quantile of interest when p_value_method == "quantile". Defaults to 1/2, i.e.~the median.

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)
X_eta <- apply(X, MARGIN = 1, FUN = function(x) 1 / (1 + exp(-eta(x))))
y <- as.numeric(runif(n) < X_eta)
get_p_value(p_value_method = "classification", X, y, x0 = c(1, 1), tau = 0.6)
get_p_value(p_value_method = "classification", X, y, x0 = c(1, 1), tau = 0.9)

X_eta <- apply(X, MARGIN = 1, FUN = eta)
y <- X_eta + rcauchy(n)
get_p_value(p_value_method = "quantile", X, y, x0 = c(1, 1), tau = 1/2)
get_p_value(p_value_method = "quantile", X, y, x0 = c(1, 1), tau = 3)
get_p_value(p_value_method = "quantile", X, y, x0 = c(1, 1), tau = 3, theta = 0.95)