fusem: The scale equivariant functional M-estimator

Description

Compute the scale equivariant functional M-estimator as described in Centofanti et al. (2023).

Usage

fusem(
  X,
  family = "bisquare",
  eff = 0.95,
  maxit = 50,
  tol = 1e-04,
  mu0_g = NULL,
  sig0_g = NULL
)

Value

A list containing the following arguments:

mu: The scale equivariant functional M-estimator .
mu0_g: mu0_g.
sig0_g: sig0_g.

Arguments

X: Either an object of class fdata for monodimensional functional data or an object of class fdata2d for bi-dimensional functional data.
family: The family of loss function for the calculation of the equivariant functional M-estimator. The values allowed are "bisquare" for the bisquare or Tukey's biweight family of loss functions; "huber" for the the Huber's family of loss functions; "optimal" for the optimal family of loss functions; "hampel" for the the Hampel's family of loss functions; "median" for the median loss function. A non-robust functional estimator of the mean based on the standard least squares loss function is used with the value "mean". Default is "bisquare".
eff: Asymptotic efficiency of the equivariant functional M-estimator. When family is either "mean" or "median", eff is ignored.
maxit: The maximum number of iterations allowed in the re-weighted least-squares algorithm to compute the equivariant functional M-estimator.
tol: The tolerance for the stopping condition of the re-weighted least-squares algorithm to compute the equivariant functional M-estimator. The algorithm stops when the relative variation of the weighted norm sum between two consecutive iterations is less than tol.
mu0_g: Initial estimate used in re-weighted least-squares algorithm to compute the equivariant functional M-estimator. If NULL the standard non-robust functional mean is used. Default is NULL.
sig0_g: Estimate of the standard error of X. If NULL, the functional mean is used. Default is NULL.

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")
X_fdata<-data_out$X_fdata
per_list_median<-fusem(X_fdata)