simulate_data: Simulate data for Robust Functional ANOVA

Description

Generate synthetic data as in the simulation study of Centofanti et al. (2023) with the addition of the case of bi-variate functional data. All the details are in Centofanti et al. (2023).

Usage

simulate_data(
  scenario = "one-way",
  mean = "M1",
  con = "C0",
  p = 0.1,
  M = 1,
  n_i = 25,
  k_1 = 3,
  k_2 = 3,
  alpha = 0,
  beta = 0,
  sd = 0.01,
  grid = seq(0, 1, length.out = 30),
  err = "s"
)

Value

A list containing the following arguments:

X_fdata: The generated functional data.
label_1: The vector of containing group label corresponding to the first main effect.
label_2: The vector of containing group label corresponding to the second main effect. For one-way ANOVA, it is NULL.

Arguments

scenario: A character strings indicating the scenario considered. It could be "one-way", "two-way", "one-way surface" and "two-way surface".
mean: A character strings indicating the type of mean function in one-way ANOVA. It could be "M1", "M2", and "M3".
con: A character strings indicating the type of contamination function. It could be "C0", for no contamination, "C1", "C2", "C3", "C4", "C5", and "C6".
p: The parameter related to the bernoulli variable in the contamination function.
M: The contamination size constant.
n_i: The number of observation for each group.
k_1: The number of level for the first main effect.
k_2: The number of level for the second main effect. For One-way ANOVA, it is ignored.
alpha: The parameter a in the Two-way ANOVA scenarios. For One-way ANOVA, it is ignored.
beta: The parameter b in the Two-way ANOVA scenarios. For One-way ANOVA, it is ignored.
sd: The sigma parameter in the covariance of the error function.
grid: The grid over which the functional data are observed.
err: The direction of the dependence in the error function for the case of bi-variate functional data. It could be either "s", for dependence along the first dimension or "t" for dependence along the second dimension.

References

Centofanti, F., Colosimo, B. M., Grasso, M. L., Menafoglio, A., Palumbo, B., & Vantini, S. (2023). Robust functional ANOVA with application to additive manufacturing. Journal of the Royal Statistical Society Series C: Applied Statistics, 72(5), 1210-1234.

Examples

Run this code

library(rofanova)
data_out<-simulate_data(scenario="one-way")
label_1=data_out$label_1
X_fdata<-data_out$X_fdata
B=10
cores=1
per_list_median<-rofanova(X_fdata,label_1,B = B,family="median",cores=cores)
pvalue_median_vec<-per_list_median$pval_vec
per_list_huber<-rofanova(X_fdata,label_1,B = B,family="huber",cores=cores)
pvalue_huber_vec<-per_list_huber$pval_vec
per_list_bisquare<-rofanova(X_fdata,label_1,B = B,family="bisquare",cores=cores)
pvalue_bisquare_vec<-per_list_bisquare$pval_vec
per_list_hampel<-rofanova(X_fdata,label_1,B = B,family="hampel",cores=cores)
pvalue_hampel_vec<-per_list_hampel$pval_vec
per_list_optimal<-rofanova(X_fdata,label_1,B = B,family="optimal",cores=cores)
pvalue_optimal<-per_list_optimal$pval