Supervised, Semi-Supervised, and Unsupervised Frameworks for Robust Anomaly Detection in Econometric Models

Anomalies in econometric data arise from measurement error, rare shocks and structural change and may distort identification, bias estimation and invalidate standard inference. Because anomaly labels are often incomplete, selectively observed or endogenous, anomaly detection cannot be treated as a purely supervised prediction task. This chapter provides a unified econometric review of supervised, semi-supervised and unsupervised paradigms, covering influence diagnostics, robust regression, outlier tests, one-class methods, isolation-based algorithms and representation learning. The discussion emphasizes robustness to contamination, misspecification and regime instability, connecting classical diagnostics with modern machine learning approaches. Practical guidance is provided on selecting appropriate paradigms, interpreting anomaly scores as screening tools and addressing inference challenges following data-dependent detection.