Comparison of Sample, Shrinkage, and Robust Covariance Estimators with Synthetic Gaussian Data

Authors

  • Dwi Handoko Department of Informatics Management, Politeknik Negeri Lampung Author
  • Dian Meilantika✉ Department of Informatics Management, Politeknik Negeri Lampung Author
Diajukan 15 Okt 2025 Diterbitkan 31 Des 2025
DOI: https://doi.org/10.59025/e4a8e8de

Keywords:

synthetic data, covariance estimation, Ledoit-Wolf shrinkage, Minimum Covariance Determinant, Monte Carlo simulation

Abstract

Evaluating methods in data science faces a fundamental obstacle: real data rarely provide complete ground truth, making it difficult to measure estimator accuracy objectively. This study constructs a synthetic-data-based evaluation framework and applies it to a case study of covariance matrix estimation for multivariate Gaussian data. A Monte Carlo experiment with 100 iterations compares three estimators — sample covariance, Ledoit-Wolf shrinkage, and Minimum Covariance Determinant (MCD) — across three scenarios: baseline without contamination, 10% outlier contamination from N(5,I), and 20% Gaussian noise with standard deviation of 2. The relative Frobenius error against the population matrix serves as the main metric. Results show the shrinkage estimator dominates in two of three scenarios with mean errors of 0.09 (baseline), 0.21 (outlier), and 0.18 (noise), while the sample covariance rises up to fourfold under outlier contamination. MCD demonstrates superior robustness to outliers but is less optimal under Gaussian noise. The findings strengthen the position of synthetic data as a reproducible, controllable instrument that can systematically map the robustness profile of methods.

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How to Cite

Comparison of Sample, Shrinkage, and Robust Covariance Estimators with Synthetic Gaussian Data. (2025). Journal of Technology and Data Science, 3(2), 258-269. https://doi.org/10.59025/e4a8e8de