稳健因子分析方法的构建及比较研究

由于传统因子分析方法对离群值较敏感，导致计算结果与实际不相符。针对这一现象，本文运用FAST-MCD方法对传统因子分析方法进行改进，构建出因子分析的稳健算法，以克服离群值的影响，并对此方法进行了模拟和实证分析。模拟和实证分析结果均表明：因子旋转前后，当数据中不存在离群值时，传统因子分析与稳健因子分析得到的结果基本保持一致；当数据中存在离群值时，运用传统因子分析得到的结果出现较大变化，而运用稳健因子分析方法得到的结果基本不变，这说明相对于传统因子分析方法，稳健因子分析方法能有效抵抗离群值的影响，具有良好的抗干扰性和高抗差性。

The Formation and Comparison of Robust Factor Analysis Method

The outcome from the traditional factor analysis method easily deviates from the fact since it is sensitive to outliers. In order to fix the problem, we improved the traditional factor analysis method by utilizing FAST-MCD and put forward the robust algorithm of factor analysis to avoid the disturbance from outliers, then made the digital simulation and the empirical analysis on the basis of robust algorithm of factor analysis. We found that the results of the traditional factor analysis and the robust factor analysis were basically the same whether the factor was rotated or not when there were no outliers in the data; the results from the traditional factor analysis changed considerably when there were outliers in data in comparison with no outliers. However, the results from robust factor analysis remained consistent whether there the outliers were or not. This comparison showed that the robust factor analysis method, which had good anti-interference and high reliability, could efficiently avoid the disturbance from the outliers.