functional_filter function

Finds functional componentwise outliers

It finds functional componentwise outliers as described in Capezza et al. (2024).

functional_filter(
  mfdobj,
  method_pca = "ROBPCA",
  alpha = 0.95,
  fev = 0.999,
  delta = 0.1,
  alpha_binom = 0.99,
  bivariate = TRUE,
  max_proportion_componentwise = 0.5
)

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.
• alpha: Probability value such that only values of functional distances greater than the alpha-quantile of the Chi-squared distribution, with a number of degrees of freedom equal to the number of principal components selected by fev, are considered to determine the proportion of flagged componentwise outliers. Default value is 0.95, as recommended by Agostinelli et al. (2015). See Capezza et al. (2024) for more details.
• fev: Number between 0 and 1 denoting the fraction of variability that must be explained by the principal components to be selected to calculate functional distances after applying RoMFPCA on mfdobj. Default is 0.999.
• delta: Number between 0 and 1 denoting the parameter of the Binomial distribution whose alpha_binom-quantile determines the threshold used in the bivariate filter. Given the i-th observation and the j-th functional variable, the number of pairs flagged as functional componentwise outliers in the i-th observation where the component (i, j) is involved is compared against this threshold to identify additional functional componentwise outliers to the ones found by the univariate filter. Default is 0.1, recommended as conservative choice by Leung et al. (2017). See Capezza et al. (2024) for more details.
• alpha_binom: Probability value such that the alpha-quantile of the Binomial distribution is considered as threshold in the bivariate filter. See delta and Capezza et al. (2024) for more details. Default value is 0.99.
• bivariate: If TRUE, both univariate and bivariate filters are applied. If FALSE, only the univariate filter is used. Default is TRUE.
• max_proportion_componentwise: If the functional filter identifies a proportion of functional componentwise outliers larger than max_proportion_componentwise, for a given observation, then it is considered as a functional casewise outlier. Default value is 0.5.

Returns

A list with two elements. The first element is an mfd object containing the original observation in the mfdobj input, but where the basis coefficients of the components identified as functional componentwise outliers are replaced by NA. The second element of the list is a list of numbers, with length equal to the number of functional variables in mfdobj. Each element of this list contains the observations of the flagged functional componentwise outliers for the corresponding functional variable.

Examples

## Not run:

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

References

Agostinelli, C., Leung, A., Yohai, V. J., and Zamar, R. H. (2015). Robust estimation of multivariate location and scatter in the presence of componentwise and casewise contamination. Test, 24(3):441–461.

Capezza, C., Centofanti, F., Lepore, A., Palumbo, B. (2024) Robust Multivariate Functional Control Chart. Technometrics, 66(4):531--547, doi:10.1080/00401706.2024.2327346.

Leung, A., Yohai, V., and Zamar, R. (2017). Multivariate location and scatter matrix estimation under componentwise and casewise contamination. Computational Statistics & Data Analysis, 111:59–76.

Author(s)

C. Capezza, F. Centofanti