Selecting the Number of Principal Components in Functional Data

Area of Science:

• Statistics
• Functional Data Analysis

Background:

• Functional principal component analysis (FPCA) is a key dimension reduction technique for functional data.
• Existing methods face challenges with sparse, dense, and measurement-error-contaminated functional data.

Purpose of the Study:

• To develop novel information criteria for selecting the number of principal components in functional data analysis.
• To address challenges posed by sparse, dense, and measurement-error-contaminated functional data.

Main Methods:

• Proposed a Bayesian information criterion (BIC) based on marginal modeling for consistent component selection.
• Developed an Akaike information criterion (AIC) for dense functional data using expected Kullback-Leibler information.
• Investigated the consistency of Bai & Ng (2002) criteria for dense functional data with undersmoothing.

Main Results:

• The proposed BIC consistently selects the number of principal components for both sparse and dense functional data.
• The proposed AIC and BIC criteria significantly outperform existing methods in simulations.
• Criteria developed for dense data also demonstrated strong performance on sparse data.

Conclusions:

• The novel information criteria provide a robust and accurate method for principal component selection in functional data analysis.
• These criteria offer improved performance over existing methods, particularly for challenging data types.
• The findings are illustrated with an application to colon carcinogenesis data.