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 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.

中文翻译：

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多通道因子分析：可识别性和渐进性


最近的工作（Ramírez 等人，2020）引入了多通道因子分析 (MFA)，作为因子分析对多通道数据的扩展，允许所有通道共有的潜在因子以及每个通道特有的因子。本文验证了 MFA 协方差模型并分析了 MFA 估计量的统计特性。特别是，对不同潜在因素结构下的模型可识别性进行了彻底的研究，并获得了 MFA 通用全局可识别性的充分条件。这些可识别性条件的发展使得能够对通过最大化高斯似然获得的估计量进行渐近分析，即使在潜在因子分布的错误指定下，这些估计量也被证明是一致且渐近正态的。