Influence Analysis in Principal Component Analysis Through Power-Series Expansions

ABSTRACT

In influence analysis several problems arise in the field of Principal Components when applying different sample versions. Among these are the difficulty of determining a certain correspondence between the eigenvalues before and after the deletion of observations, the choice of the sign of the eigenvectors and the computational problem derived from the resolution of a great number of eigenproblems. In this article, such problems are discussed from the joint influence point of view and a solution is proposed by using approximations. Furthermore, the influence on a new parameter of interest is introduced: the proportion of variance explained by a set of principal components.

Keywords:

• Joint influence
• Power-series expansions
• Principal component
• Proportion of variance

Mathematics Subject Classification:

• 62H25
• 62H99

Acknowledgments

The authors would like to thank the referee for his valuable suggestion.

Work on this article was partially supported by the Ministerio de Ciencia y Tecnología of Spain (Plan Nacional I+D+I, BMF 2001-3844) and the Ministerio de Educación y Ciencia of Spain (MTM2004-01433).