Sensitivity Coefficient in Principal Component Analysis: Robust Case

Abstract

In the classical principal component analysis (PCA), the empirical influence function for the sensitivity coefficient ρ is used to detect influential observations on the subspace spanned by the dominants principal components. In this article, we derive the influence function of ρ in the case where the reweighted minimum covariance determinant (MCD¹) is used as estimator of multivariate location and scatter. Our aim is to confirm the reliability in terms of robustness of the MCD¹ via the approach based on the influence function of the sensitivity coefficient.

Keywords:

• Influence function
• Principal component analysis
• Reweighted minimum covariance determinant
• Sensitivity coefficient

Mathematics Subject Classification:

• 62H25
• 62F35

Acknowledgments

We wish to thank the reviewer for helpful comments.