fusem: The scale equivariant functional M-estimator

In rofanova: Robust Functional Analysis of Variance

Description

Compute the scale equivariant functional M-estimator as described in Centofanti et al. (2021).

Usage

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

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.

Value

A list containing the following arguments:

• mu: The scale equivariant functional M-estimator .

• mu0_g: mu0_g.

• sig0_g: sig0_g.

References

Centofanti, F., Colosimo, B.M., Grasso, M.L., Menafoglio, A., Palumbo, B., Vantini, S. (2021). Robust Functional ANOVA with Application to Additive Manufacturing. arXiv preprint arXiv:2112.10643.

See Also

rofanova funmad

Examples

library(rofanova)
data_out<-simulate_data(scenario="one-way")
X_fdata<-data_out$X_fdata
per_list_median<-fusem(X_fdata)

rofanova documentation built on Jan. 22, 2022, 1:06 a.m.