RoMFDI {funcharts}

Robust Multivariate Functional Data Imputation (RoMFDI)

Description

It performs Robust Multivariate Functional Data Imputation (RoMFDI) as in Capezza et al. (2022).

Usage

RoMFDI(
  mfdobj,
  method_pca = "ROBPCA",
  fev = 0.999,
  n_dataset = 3,
  update = TRUE,
  niter_update = 10,
  alpha = 0.8
)

Arguments

mfdobj

A multivariate functional data object of class mfd.

method_pca

The method used in rpca_mfd to perform robust multivariate functional principal component analysis (RoMFPCA). See rpca_mfd. Default is "ROBPCA".

fev

Number between 0 and 1 denoting the proportion of variability that must be explained by the principal components to be selected for dimension reduction after applying RoMFPCA on the observed components to impute the missing ones. Default is 0.999.

n_dataset

To take into account the increased noise due to single imputation, the proposed RoMFDI allows multiple imputation. Due to the presence of the stochastic component in the imputation, it is worth explicitly noting that the imputed data set is not deterministically assigned. Therefore, by performing several times the RoMFDI in the imputation step of the RoMFCC implementation, the corresponding multiple estimated RoMFPCA models could be combined by averaging the robustly estimated covariance functions, thus performing a multiple imputation strategy as suggested by Van Ginkel et al. (2007). Default is 3.

update

The RoMFDI performs sequential imputation of missing functional components. If TRUE, Robust Multivariate Functional Principal Component Analysis (RoMFPCA) niter_update is updated times during the algorithm. If FALSE, the RoMFPCA used for imputation is always the same, i.e., the one performed on the original data sets containing only the observations with no missing functional components. Default is TRUE.

niter_update

The number of times the RoMFPCA is updated during the algorithm. It applies only if update is TRUE. Default value is 10.

alpha

This parameter measures the fraction of outliers the RoMFPCA algorithm should resist and is used only if method_pca is "ROBPCA". Default is 0.8.

Value

A list with n_dataset elements. Each element is an mfd object containing mfdobj with stochastic imputation of the missing components.

References

Capezza, C., Centofanti, F., Lepore, A., Palumbo, B. (2022) Robust Multivariate Functional Control Charts. arXiv:2207.07978v

Van Ginkel, J. R., Van der Ark, L. A., Sijtsma, K., and Vermunt, J. K. (2007). Two-way imputation: a bayesian method for estimating missing scores in tests and questionnaires, and an accurate approximation. Computational Statistics & Data Analysis, 51(8):4013–-4027.

Examples

## Not run: 
library(funcharts)
mfdobj <- get_mfd_list(air, grid = 1:24, n_basis = 13, lambda = 1e-2)
out <- functional_filter(mfdobj)
mfdobj_imp <- RoMFDI(out$mfdobj)

## End(Not run)