Robust Covariance Matrix Estimation for High-Dimensional Compositional Data with Application to Sales Data Analysis.

Area of Science:

• Statistics
• Data Analysis

Background:

• Compositional data analysis is crucial in various fields requiring data standardization.
• Estimating covariance matrices is fundamental for high-dimensional compositional data.
• Current methods often rely on restrictive Gaussian or sub-Gaussian assumptions.

Purpose of the Study:

• To develop a robust covariance estimation method for high-dimensional compositional data.
• To address the limitations of existing methods that assume Gaussian distributions.
• To provide a statistically sound procedure for sparse compositional data.

Main Methods:

• Proposed a robust composition adjusted thresholding covariance procedure.
• Utilized Huber-type M-estimation for robust estimation.
• Introduced a cross-validation procedure for tuning parameter selection.

Main Results:

• The method effectively estimates sparse covariance structures in high-dimensional compositional data.
• Theoretical guarantees for convergence rates and signal recovery were established under bounded fourth moment conditions.
• Cross-validation procedure demonstrated theoretical guarantees in high-dimensional settings.

Conclusions:

• The proposed robust method enhances the analysis of high-dimensional compositional data.
• The method overcomes restrictive distributional assumptions, offering broader applicability.
• Effectiveness validated through simulations and a real-world sales data application.