For factor analysis, many estimators, starting with the maximum likelihood estimator, have been developed, and the statistical properties of most estimators have been well explored. 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 yet to be discussed. To explain this unexpected behavior theoretically, we establish the consistency of the MDFA estimator for factor analysis. That is, we show that the MDFA estimator converges to the same limit as other consistent estimators of factor analysis.

翻译：对于因子分析，从最大似然估计量开始，已经发展出许多估计量，并且大多数估计量的统计性质已得到充分研究。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，但经验表明其行为类似于因子分析的其他相合估计量，而非主成分分析。由于MDFA估计量无法表述为经典的M-估计量，其统计性质尚未得到充分讨论。为从理论上解释这一意外现象，我们建立了MDFA估计量在因子分析中的相合性。即证明MDFA估计量收敛于因子分析其他相合估计量的相同极限。