Information criteria for latent factor models: a study on factor pervasiveness and adaptivity.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• High-dimensional data analysis often relies on latent factor models.
• Principal Component Analysis (PCA) is a common method for estimating latent factors.
• Existing information criteria may struggle with weak factor pervasiveness and varying factor strengths.

Purpose of the Study:

• To develop and validate a novel information criterion for determining the number of latent factors in high-dimensional models.
• To provide theoretical guarantees for the estimation accuracy of latent factor scores.
• To address limitations of current methods when factor strengths are weak or heterogeneous.

Main Methods:

• Theoretical analysis of estimation errors in Principal Component Analysis (PCA).
• Development of a new penalty specification for information criteria, adaptive to factor pervasiveness.
• Construction of theoretical examples and extensive numerical simulations.

Main Results:

• Established theoretical results on the estimation accuracy of latent factor scores under general conditions.
• Demonstrated the validity of the proposed adaptive information criterion.
• Identified scenarios where no information criterion can consistently estimate latent factors due to weak factor strength.

Conclusions:

• The proposed adaptive information criterion offers improved performance for high-dimensional latent factor models.
• The method is robust to varying factor strengths and weak factor pervasiveness.
• Theoretical and empirical evidence supports the effectiveness of the new criterion.