Information Criterion-Based Rank Estimation Methods for Factor Analysis: A Unified Selection Consistency Theorem and Numerical Comparison
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914891499044864 |
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| author | Morimoto, Toshinari Hung, Hung Huang, Su-Yun |
| author_facet | Morimoto, Toshinari Hung, Hung Huang, Su-Yun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Information Criterion-Based Rank Estimation Methods for Factor Analysis: A Unified Selection Consistency Theorem and Numerical Comparison Morimoto, Toshinari Hung, Hung Huang, Su-Yun Statistics Theory 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. |
| title | Information Criterion-Based Rank Estimation Methods for Factor Analysis: A Unified Selection Consistency Theorem and Numerical Comparison |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2407.19959 |