For factor analysis, many estimators, starting with the maximum likelihood estimator, are developed, and the statistical properties of most estimators are well discussed. In the early 2000s, a new estimator based on matrix factorization, called Matrix Decomposition Factor Analysis (MDFA), was developed. Although the estimator is obtained by minimizing the principal component analysis-like loss function, this estimator empirically behaves like other consistent estimators of factor analysis, not principal component analysis. Since the MDFA estimator cannot be formulated as a classical M-estimator, the statistical properties of the MDFA estimator have not yet been discussed. To explain this unexpected behavior theoretically, we establish the consistency of the MDFA estimator as the factor analysis. That is, we show that the MDFA estimator has the same limit as other consistent estimators of factor analysis.

翻译：对于因子分析，许多估计量（从最大似然估计量开始）已被开发出来，且大多数估计量的统计性质已得到充分讨论。在21世纪初，一种基于矩阵分解的新估计量——矩阵分解因子分析（MDFA）被提出。尽管该估计量通过最小化类似主成分分析的损失函数获得，但在经验上其行为类似于因子分析的其他一致估计量，而非主成分分析。由于MDFA估计量无法被表述为经典M-估计量，其统计性质尚未得到探讨。为从理论上解释这一意外行为，我们确立了MDFA估计量作为因子分析的一致性。即，我们证明MDFA估计量具有与其他因子分析一致估计量相同的极限。