Searching for the core variables in principal components analysis

Abstract

In this article, we introduce a procedure for selecting variables in principal components analysis. The procedure was developed to identify a small subset of the original variables that best explain the principal components through nonparametric relationships. There are usually some noisy uninformative variables in a dataset, and some variables that are strongly related to each other because of their general interdependence. The procedure is designed to be used following the satisfactory initial use of a principal components analysis with all variables, and its aim is to help to interpret underlying structures. We analyze the asymptotic behavior of the method and provide some examples.