On statistical inference with high-dimensional sparse CCA

Area of Science:

• Statistics
• High-Dimensional Data Analysis
• Multivariate Analysis

Background:

• Canonical Correlation Analysis (CCA) is crucial for understanding relationships between variable sets.
• High-dimensional data presents challenges for traditional CCA due to the curse of dimensionality.
• Sparsity in high-dimensional data requires specialized methods for robust analysis.

Purpose of the Study:

• To develop asymptotically exact inference for canonical correlation directions and strengths.
• To address challenges posed by high-dimensional vectors and sparsity restrictions.
• To improve the accuracy of initial estimators through bias correction.

Main Methods:

• Novel representation of the Canonical Correlation Analysis problem.
• Development of a one-step bias correction procedure.
• Asymptotic analysis under sparsity and structural restrictions of nuisance parameters.

Main Results:

• Achieved asymptotically exact inference for leading canonical correlation directions and strengths.
• Proposed a bias-corrected method that is adaptive to structural restrictions.
• Demonstrated theoretical guarantees through extensive numerical studies.

Conclusions:

• The novel approach provides accurate estimation in high-dimensional, sparse settings.
• The bias correction method enhances the reliability of CCA results.
• The findings are supported by robust theoretical and empirical evidence.