Modern datasets in genomics, finance, and imaging often involve thousands of variables and arefrequently contaminated with outliers. Classical correlation measures, such as Pearson’s coefficient, are highly sensitive to such contamination and fail to scale effectively in high-dimensional settings. This thesis presents a data-driven framework for robust and scalable correlation estimation designed to address these challenges. We first review existing estimators—including Pearson, Spearman, MCD, SSCM, and GK—and evaluate them across key criteria: robustness (breakdown point), influence function, computational complexity, and positive semi-definiteness (PSD). Limitations in their performance under contamination and high dimensionality motivate the introduction of the wrapping transformation, a recent robust univariate method proposed by Raymaekers and Rousseeuw in 2021[1]. We explore the theoretical properties of wrapping, including its bounded influence function, redescending ψ-function, and its guarantee to preserve PSD correlation matrices. Through extensive simulations (10,000 replicates per setting), we assess the performance of various estimators across clean and contaminated datasets, with contamination levels up to 10% and dimensions ranging from 5 to 1000. The results show that the wrapping-based estimator achieves high efficiency in clean settings (ARE ≈ 90%) and maintains low bias, low MSE, and numerical stability under contamination. It scales linearly with dimensionality (O(dn)) and requires no eigenvalue correction to maintain PSD, making it highly suitable for modern high-dimensional applications. This work concludes that wrapping offers a principled, robust, and scalable alternative to classical correlation measures—bridging the gap between statistical theory and real-world, noisy, high-dimensional data analysis.
