FDOTT (version 0.1.0)

simulate_finite_FDOTT: Simulations for FDOTT

Description

Perform simulations for the test statistic used in FDOTT.

Usage

simulate_finite_FDOTT(mu, costm, n, H0 = "*", num.sim = 1000)
simulate_limit_FDOTT_null(
  mu,
  costm,
  n = NULL,
  delta = NULL,
  H0 = "*",
  num.sim = 1000,
  method = c("plug-in", "bootstrap-deriv", "bootstrap-m"),
  m.p = 0.5,
  mean = NULL
)
simulate_limit_FDOTT_alt(mu, costm, delta, H0 = "*", num.sim = 1000)

Value

A vector containing the simulated samples.

Arguments

mu

matrix (row-wise) or nested list containing \(K\) probability vectors.

costm

semi-metric cost matrix \(c \in \mathbb{R}^{N \times N}\).

n

samples sizes. Must be of the same structure as mu.

H0

null hypothesis, see FDOTT for more information.

num.sim

number of samples to draw from the limiting null distribution.

delta

asymptotic sample size ratios. Must be of the same structure as mu.

method

the method to use to simulate from the null distribution.

m.p

exponent \(p \in (0, 1)\) used for method = "bootstrap-m".

mean

mean of the Gaussians appearing in the limiting distribution. Must be of the same structure as mu.

Details

See FDOTT for the definition of the test statistic and more details.

simulate_finite_FDOTT simulates from the finite sample distribution.

simulate_limit_FDOTT_null and simulate_limit_FDOTT_alt simulate from the limiting distribution under the null or alternative, respectively.

All these simulations can be done in parallel via future::plan and the progress can be shown with progressr::with_progress.

Examples

# enable txt progressbar
progressr::handlers("txtprogressbar")
# enable parallel computation
if (requireNamespace("future")) {
    future::plan(future::multisession)
}

K <- 3
N <- 2
costm <- cost_matrix_lp(1:N)

# use higher values for better approximation
num.sim <- 10
n <- rep(300, K)

delta <- rep(1 / K, K)

# under one-way null
mu <- matrix(1 / N, K, N, TRUE)

set.seed(123)
lhs <- simulate_finite_FDOTT(mu, costm, n, num.sim = num.sim)
rhs <- simulate_limit_FDOTT_null(mu, costm, delta = delta, num.sim = num.sim)

h1 <- density(lhs)
h2 <- density(rhs)
plot(h1$x, h1$y, xlim = range(h1$x, h2$x), ylim = range(h1$y, h2$y), type = "l",
     col = "red", xlab = "x", ylab = "density", main = "KDEs")
lines(h2$x, h2$y, col = "blue")
legend("topright", c("Finite", "Limit"), col = c("red", "blue"), pch = 15)

# under one-way alternative
mu[2, ] <- 1:N / sum(1:N)

set.seed(123)
lhs <- simulate_finite_FDOTT(mu, costm, n, num.sim = num.sim)
rhs <- simulate_limit_FDOTT_alt(mu, costm, delta, num.sim = num.sim)

h1 <- density(lhs)
h2 <- density(rhs)
plot(h1$x, h1$y, xlim = range(h1$x, h2$x), ylim = range(h1$y, h2$y), type = "l",
     col = "red", xlab = "x", ylab = "density", main = "KDEs")
lines(h2$x, h2$y, col = "blue")
legend("topright", c("Finite", "Limit"), col = c("red", "blue"), pch = 15)
# \dontshow{
## R CMD check: make sure any open connections are closed afterward
if (requireNamespace("future") && !inherits(future::plan(), "sequential")) future::plan(future::sequential)
# }