Multi-Channel Factor Analysis: Identifiability and Asymptotics

TL;DR

This paper validates the covariance model of Multi-Channel Factor Analysis (MFA), analyzes the statistical properties of its estimators, and establishes conditions for their identifiability, consistency, and asymptotic normality.

Contribution

It provides the first thorough identifiability conditions for MFA and analyzes the asymptotic behavior of its estimators under various latent factor structures.

Findings

Identifiability conditions for MFA are established.

MFA estimators are shown to be consistent and asymptotically normal.

The analysis holds even under latent factor distribution misspecification.

Abstract

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.