Multi-channel factor analysis: identifiability and asymptotics

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URI: https://hdl.handle.net/10902/33946
ISSN: 1053-587X
ISSN: 1941-0476
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Autoría
Stanton, Gray; Ramírez García, David; Santamaría Caballero, Luis IgnacioAutoridad Unican; Scharf, Louis; Wang, Haonan
Fecha
2024-07-12
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© 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Publicado en
IEEE Transactions on Signal Processing, 2024, 72, 3562-3577
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Institute of Electrical and Electronics Engineers, Inc.
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Palabras clave
Asymptotic normality
Consistency
Factor analysis (FA)
Identifiability
Multi-channel factor analysis (MFA)
Resumen/Abstract
Recent work (Ramírez et al. 2020) 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 forgeneric global identifiability of MFA are obtained. The develop ment of these identifiability conditions enables asymptotic analy sis 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.
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