Generalized spherical principal component analysis

Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal component analysis, a new robust version of principal component analysis that is based on the generalized spatial sign covariance matrix. Theoretical properties of the proposed method including influence functions, breakdown values and asymptotic efficiencies are derived. These theoretical results are complemented with an extensive simulation study and two real-data examples. We illustrate that generalized spherical principal component analysis can combine great robustness with solid efficiency properties, in addition to a low computational cost.