Multi-Channel Factor Analysis: Identifiability and Asymptotics
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914888960442368 |
|---|---|
| author | Stanton, Gray Ramírez, David Santamaria, Ignacio Scharf, Louis Wang, Haonan |
| author_facet | Stanton, Gray Ramírez, David Santamaria, Ignacio Scharf, Louis Wang, Haonan |
| contents | Recent work by Ramírez et al. [2] has introduced Multi-Channel Factor Analysis (MFA) as an extension of factor analysis to multi-channel data that allows for latent factors common to all channels as well as factors specific to each channel. This paper validates the MFA covariance model and analyzes the statistical properties of the MFA estimators. In particular, a thorough investigation of model identifiability under varying latent factor structures is conducted, and sufficient conditions for generic global identifiability of MFA are obtained. The development of these identifiability conditions enables asymptotic analysis of estimators obtained by maximizing a Gaussian likelihood, which are shown to be consistent and asymptotically normal even under misspecification of the latent factor distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18896 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-Channel Factor Analysis: Identifiability and Asymptotics Stanton, Gray Ramírez, David Santamaria, Ignacio Scharf, Louis Wang, Haonan Signal Processing Statistics Theory Recent work by Ramírez et al. [2] has introduced Multi-Channel Factor Analysis (MFA) as an extension of factor analysis to multi-channel data that allows for latent factors common to all channels as well as factors specific to each channel. This paper validates the MFA covariance model and analyzes the statistical properties of the MFA estimators. In particular, a thorough investigation of model identifiability under varying latent factor structures is conducted, and sufficient conditions for generic global identifiability of MFA are obtained. The development of these identifiability conditions enables asymptotic analysis of estimators obtained by maximizing a Gaussian likelihood, which are shown to be consistent and asymptotically normal even under misspecification of the latent factor distribution. |
| title | Multi-Channel Factor Analysis: Identifiability and Asymptotics |
| topic | Signal Processing Statistics Theory |
| url | https://arxiv.org/abs/2407.18896 |