# Simulations for `FDOTT` Perform simulations for the test statistic used in `FDOTT`. ```r 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) ``` ## 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`. ## Returns A vector containing the simulated samples. ## 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 ```r # 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) ```

sim_fac function