Information Criterion-Based Rank Estimation Methods for Factor Analysis: A Unified Selection Consistency Theorem and Numerical Comparison

TL;DR

This paper presents a unified theoretical framework for the consistency of information criterion-based rank estimators in factor analysis, supported by extensive simulations comparing their performance with other methods.

Contribution

It establishes a unified theorem on selection consistency based on gap conditions and provides comprehensive numerical comparisons of different rank estimators.

Findings

Unified gap conditions determine rank selection consistency.

Information criterion-based estimators perform reliably under certain conditions.

Comparative analysis highlights strengths and limitations of various estimators.

Abstract

Over the years, numerous rank estimators for factor models have been proposed in the literature. This article focuses on information criterion-based rank estimators and investigates their consistency in rank selection. The gap conditions serve as necessary and sufficient conditions for rank estimators to achieve selection consistency under the general assumptions of random matrix theory. We establish a unified theorem on selection consistency, presenting the gap conditions for information criterion-based rank estimators with a unified formulation. To validate the theorem's assertion that rank selection consistency is solely determined by the gap conditions, we conduct extensive numerical simulations across various settings. Additionally, we undertake supplementary simulations to explore the strengths and limitations of information criterion-based estimators by comparing them with other types of rank estimators.