Abstract: Traditional multivariable analysis method, for example, principal component analysis (PCA) method and factor analysis method, are common in calculating the mean vector, the covariance matrix of sample and other variables. When there are no outliers in the sample, these methods can get good results. But when there are outliers in the sample, these methods are easily affected by them. This paper focuses on the study of the most popular FAST-MCD method which is improved to overcome its shortcoming, constructs robust mean vector and robust covariance matrix which is applied in PCA method. From the result of simulation and empirical study, the improved method and the new robust estimator are good for resisting outliers and decrease their influence greatly.

Key words: Outliers, FAST-MCD algorithm, PCA, Robust PCA