Unveiling outliers with robust covariance matrix estimation: a shrinkage approach

Outlier detection is a fundamental task in statistics, crucial for identifying anomalous observations that deviate significantly from the majority of the data. This article proposes a robust shrinkage covariance matrix based on the Gnanadesikan-Kettenring estimator and develops the shrinkage Gnanadesikan-Kettenring (SGK) method, a robust outlier detection technique for high dimensional datasets. The effectiveness of the SGK method for outlier detection is comprehensively evaluated using diverse metrics and scenarios through Monte Carlo simulation. The empirical study employs success rate and false detection rate to compare its performance with existing methods across various data characteristics, including correlated and uncorrelated data generated from multivariate normal, multivariate t, and multivariate exponential distributions. Results indicate that the SGK method consistently achieves a high success rate in identifying contaminated observations with a significantly lower false detection rate compared to other methods. Despite being non-affine equivariant, the SGK method maintains similar performance under affinely transformed data and exhibits exceptional resistance to contamination across datasets of varying sizes and dimensions. Real-world applicability is confirmed through performance evaluations on benchmark datasets, where the SGK method successfully identifies known outliers.