Using observed confidence levels to perform principal component analyses

ABSTRACT

This paper focuses on applying the method of observed confidence levels to problems commonly encountered in principal component analyses. In particular, we focus on assigning levels of confidence to the number of components that explain a specified proportion of variation in the original data. Approaches based on the normal model as well as a non parametric model are explored. The usefulness of the methods are discussed using an example and an empirical study.

Keywords:

• Eigenvalue
• Eigenvector
• Multivariate analysis
• Non parametric bootstrap
• Parametric bootstrap.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 62H25; Secondary: 62G09

Acknowledgments

The authors acknowledge the comments of the reviewers which greatly improved the clarity of the presentation of this paper.