IMCD: Interval-valued data Minimum Covariance Determinant (IMCD)...

In AIDA: Analysis of Interval DAta

Interval-valued data Minimum Covariance Determinant (IMCD) estimation

Description

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

Usage

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

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*data@NObs).
cutoff	Indicates which cutoff should be considered for reweighting the estimates: "chi-squared": The traditional 97.5% Chi-Squared quantile. "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.
cor	A logical value indicating whether to return the correlation matrix. Defaults to FALSE.

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").
cor_IMCD	Estimated correlation matrix (if cor is set to TRUE).

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

# Obtain reweighted IMCD estimates using farness cutoff
credit_card_IMCD <- IMCD(credit_card_int, 
                         m = floor(nrow(credit_card_int)*0.75), 
                         cutoff = "farness", 
                         cutoff_lvl = 0.9)

AIDA documentation built on Nov. 4, 2026, 9:06 a.m.