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Interval-valued data Minimum Covariance Determinant (IMCD) estimation

Source: R/IMCD.r
IMCD.Rd

Applies an adaptation of the FAST-MCD algorithm to estimate location and scatter for interval-valued data.

Usage

IMCD(
  data,
  m = 0,
  cutoff = c("farness", "adjbox", "chi-squared", "F-dist", "raw"),
  cutoff_lvl = NULL
)

Arguments

data

An intData object containing the interval-valued dataset (macrodata).

m

An integer specifying the subset size to use for the estimation. Defaults to floor(0.75*n).

cutoff

Indicates which cutoff should be considered for reweighting the estimates:

  • "chi-squared": The traditional 97.5\

  • "raw": No reweighting.

  • "adjbox": Adjusted Boxplots (package robustbase).

  • "F-dist": The quantile of the scaled F distribution (adapted from package CerioliOutlierDetection).

  • "farness": "Farness" is estimated from the robust distance (adapted from package cellWise).

Defaults to "farness".

cutoff_lvl

A numeric value specifying the level of the cutoff to be used.

  • If cutoff="chi-squared", cutoff_lvl is the quantile of the Chi-squared distribution (default is 0.975).

  • If cutoff="adjbox", cutoff_lvl is the coefficient for the adjusted boxplot (default is 1.5).

  • If cutoff="F-dist", cutoff_lvl is the quantile of the F-distribution (default is 0.975).

  • If cutoff="farness", cutoff_lvl represents the threshold for farness, with a default of 0.99.

  • If cutoff="raw", cutoff_lvl is ignored.

If no value is provided, the function uses the default values associated with each cutoff method.

Value

A list containing the robustly estimated parameters:

mean_IMCD_c

Estimated mean of the centers of the interval data.

mean_IMCD_r

Estimated mean of the ranges of the interval data.

cov_IMCD

Estimated covariance (scatter) matrix (int_cov) for the data.

final_z

Binary vector indicating the inclusion of each observation in the reweighted subset.

cutoff

The cutoff method used for reweighting.

cutoff_value

Cutoff value used for reweighting.

robust_dist

Robust distances (IMah_dist) for each observation.

farness_probs

Farness probabilities (if cutoff is set to "farness").

References

Loureiro, C. P., Oliveira, M. R., Brito, P., & Oliveira, L. (2026). Minimum Covariance Determinant Estimator and Outlier Detection for Interval-valued Data. arXiv preprint arXiv:2604.26769. https://arxiv.org/abs/2604.26769

Adapted from https://github.com/frankp-0/fastMCD.

The case cutoff=="F-dist" is adapted from package CerioliOutlierDetection (https://cran.r-project.org/package=CerioliOutlierDetection).

Examples

# Example using creditcard dataset
data(creditcard)
credit_card_int <- creditcard$intData

credit_card_IMCD <- IMCD(credit_card_int, floor(0.75*credit_card_int@NObs), "farness", 0.9)