Sparse Gaussianized Canonical Correlation Analysis with Applications to Portfolio Analysis

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• Canonical Correlation Analysis (CCA) is crucial for identifying linear relationships between variable sets.
• Classical CCA struggles with high-dimensional and heavy-tailed data.
• Existing methods lack robustness and comprehensive consistency guarantees.

Purpose of the Study:

• To propose a novel generalization of CCA for high-dimensional data analysis.
• To introduce Sparse Gaussianized CCA (SGCCA) with enhanced properties.
• To address limitations of classical CCA in real-world data scenarios.

Main Methods:

• Developed SGCCA, a computationally efficient and conceptually simple CCA generalization.
• Incorporated sparsity and Gaussianization for improved robustness.
• Utilized semiparametric copula models for theoretical analysis.

Main Results:

• SGCCA yields sparse, nested canonical vectors and is invariant to monotone transformations.
• Demonstrated estimation and variable selection consistency under mild conditions.
• Extensive simulations confirm SGCCA's superior performance over existing methods.

Conclusions:

• SGCCA is a powerful and robust tool for high-dimensional statistical analysis.
• The method effectively handles heavy-tailed data and provides reliable variable selection.
• SGCCA offers a significant advancement for analyzing complex correlation structures, as shown in stock market analysis.