Structured functional principal component analysis.

Area of Science:

• Statistics
• Functional Data Analysis
• Statistical Modeling

Background:

• Modern observational studies require advanced statistical models.
• Existing models may not fully capture correlation structures in functional data.
• Nested and crossed designs present unique analytical challenges.

Purpose of the Study:

• To introduce a novel class of functional models.
• To extend existing models for nested and crossed designs.
• To account for inherent correlation structures in functional and image-based data.

Main Methods:

• Development of functional models incorporating nested and crossed designs.
• Inference based on functional quadratics and latent process covariance.
• A computationally efficient and scalable estimation procedure for high-dimensional data.

Main Results:

• The proposed models effectively handle complex correlation structures.
• The estimation procedure is fast and scalable for large datasets.
• Demonstrated applicability across diverse functional data types.

Conclusions:

• The new functional models provide a robust framework for analyzing complex sampling designs.
• The efficient estimation method facilitates application to high-dimensional functional data.
• These methods advance the analysis of diverse data, including accelerometer, linguistic, and EEG data.