  Recent work by Ram\'irez 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.
