Object Oriented Solution for Robust Factor Analysis

Outliers virtually exist in any datasets of any application field. To avoid the impact of outliers, we need to use robust estimators. Classical estimators of multivariate mean and covariance matrix are the sample mean and the sample covariance matrix. Outliers will affect the sample mean and the sample covariance matrix, and thus they will affect the classical factor analysis which depends on the classical estimators (Pison, G., Rousseeuw, P.J., Filzmoser, P. and Croux, C. (2003) ). So it is necessary to use the robust estimators of the sample mean and the sample covariance matrix. There are several robust estimators in the literature: Minimum Covariance Determinant estimator, Orthogonalized Gnanadesikan-Kettenring, Minimum Volume Ellipsoid, M, S, and Stahel-Donoho. The most direct way to make multivariate analysis more robust is to replace the sample mean and the sample covariance matrix of the classical estimators to robust estimators (Maronna, R.A., Martin, D. and Yohai, V. (2006) ) (Todorov, V. and Filzmoser, P. (2009) ), which is our choice of robust factor analysis. We created an object oriented solution for robust factor analysis based on new S4 classes.