power_exp: Simulation-based experiment for power analysis

In funStatTest: Statistical Testing for Functional Data

Simulation-based experiment for power analysis

Description

Computation of the statistical power (i.e. risk to reject the null hypothesis when it is false) associated to any statistics described in the package based on simulation permutation-based p-values computations. See Smida et al (2022) for more details.

Usage

power_exp(
  n_simu = 100,
  alpha = 0.05,
  n_perm = 100,
  stat = c("mo", "med"),
  n_point = 100,
  n_obs1 = 50,
  n_obs2 = 50,
  c_val = 1,
  delta_shape = "constant",
  distrib = "normal",
  max_iter = 10000,
  verbose = FALSE
)

Arguments

n_simu	integer value, number of simulations to compute the statistical power.
alpha	numerical value, between 0 and 1, type I risk level to reject the null hypothesis in the simulation. Default value is ⁠5%⁠.
n_perm	integer, number of permutation to compute the p-values.
stat	character string or vector of character string, name of the statistics for which the p-values will be computed, among "mo", "med", "wmw", "hkr", "cff".
n_point	integer value, number of points in the trajectory.
n_obs1	integer value, number of trajectories in the first sample.
n_obs2	integer value, number of trajectories in the second sample.
c_val	numeric value, level of divergence between the two samples.
delta_shape	character string, shape of the divergence between the two samples, among "constant", "linear", "quadratic".
distrib	character string, type of probability distribution used to simulate the data among "normal", "cauchy", "dexp", "student".
max_iter	integer, maximum number of iteration for the iterative simulation process.
verbose	boolean, if TRUE, enable verbosity.

Details

The c_val input argument should be strictly positive so that the null hypothesis is not verified when simulating the data (i.e. so that the two sample are not generated from the same probability distribution).

Value

a list with the following elements:

• power_res: a list of named numeric value corresponding to the power values for each statistic listed in stat input.

• pval_res: a list of named numeric values corresponding to the p-values for each simulation and each statistic listed in the stat input.

• simu_config: information about input parameters used for simulation, including n_simu, c_val, distrib, delta_shape, n_point, n_obs1, n_obs2.

Author(s)

Zaineb Smida, Ghislain DURIF, Lionel Cucala

References

Zaineb Smida, Lionel Cucala, Ali Gannoun & Ghislain Durif (2022) A median test for functional data, Journal of Nonparametric Statistics, 34:2, 520-553, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10485252.2022.2064997")}, hal-03658578

See Also

stat_mo(), stat_med(), stat_wmw(), stat_hkr(), stat_cff(), comp_stat()

Examples

# simulate a few small data for the example
res <- power_exp(
    n_simu = 20, alpha = 0.05, n_perm = 100, 
    stat = c("mo", "med", "wmw", "hkr", "cff"), 
    n_point = 25, n_obs1 = 4, n_obs2 = 5, c_val = 10, delta_shape = "constant", 
    distrib = "normal", max_iter = 10000, verbose = FALSE
)
res$power_res

funStatTest documentation built on May 29, 2024, 10:26 a.m.