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Outlier Detection for Interval-Valued Data Based on Robust Distances

Source: R/int_outliers.r
int_outliers.Rd

Identifies potential outliers in interval-valued data using robust distance-based methods with customizable cutoff criteria.

Usage

int_outliers(
  robust_dist,
  cutoff = c("farness", "adjbox", "chi-squared", "F-dist"),
  cutoff_lvl = NULL,
  p = NULL,
  z = NULL
)

Arguments

robust_dist

A numeric vector containing the robust distances for each observation.

cutoff

A character string specifying the method for setting the outlier cutoff threshold. Options include:

  • "chi-squared": Outliers are identified based on a specified Chi-Squared quantile.

  • "adjbox": Uses adjusted boxplot statistics (from robustbase) to classify outliers.

  • "F-dist": Applies a cutoff derived from the F and Beta distributions for robust outlier detection.

  • "farness": Identifies outliers based on a "farness" threshold, determined by the robust distance distribution.

Default is "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 significance level for identifying outliers (default is 0.95).

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

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

p

The number of variables in the data. Required for "chi-squared" and "F-dist" cutoff methods.

z

A binary vector indicating the subset of observations used for initial robust estimation. Required for the "F-dist" cutoff method.

Value

A list with the following components:

outliers_names

Character vector of names for observations classified as outliers.

is_outlier

Logical vector indicating whether each observation is an outlier (TRUE) or not (FALSE).

cutoff

The cutoff method used for detecting outliers.

cutoff_value

Cutoff value used for detecting outliers.

farness_probs

Numeric vector of farness probabilities for each observation (only if cutoff is set to "farness").

Details

This function classifies observations as outliers based on robust distances and user-defined cutoff methods. It supports various approaches, including Chi-Squared quantiles, adjusted boxplots, F distribution quantiles, and farness probabilities.

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

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

Examples

# Example of detecting outliers using robust distances
set.seed(42)
robust_dist <- abs(rnorm(100))
result <- int_outliers(robust_dist, cutoff="chi-squared", p=5)

# 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)
credit_card_outliers <- int_outliers(credit_card_IMCD$robust_dist, "farness", 0.9)