Outlier Detection in Contingency Tables based on Minimal Patterns

TL;DR

This paper introduces a novel outlier detection method for contingency tables using minimal patterns, which are subsets of cell counts that enable robust estimation of expected counts under classical models.

Contribution

The paper develops a new outlier detection technique based on minimal patterns, providing a practical criterion for their selection and demonstrating improved performance over existing methods.

Findings

Effective outlier detection in contingency tables demonstrated through simulations.

The method outperforms existing techniques in identifying cell count anomalies.

Real-data examples validate the approach's practical utility.

Abstract

A new technique for the detection of outliers in contingency tables is introduced. Outliers thereby are unexpected cell counts with respect to classical loglinear Poisson models. Subsets of cell counts called minimal patterns are defined, corresponding to non-singular design matrices and leading to potentially uncontaminated maximum-likelihood estimates of the model parameters and thereby the expected cell counts. A criterion to easily produce minimal patterns in the two-way case under independence is derived, based on the analysis of the positions of the chosen cells. A simulation study and a couple of real-data examples are presented to illustrate the performances of the newly developed outlier identification algorithm, and to compare it with other existing methods.