Simplification and signification of principal components

Within the framework of principal component analysis (PCA), we propose a procedure of hypothesis testing to assess the signification of the principal components and the signification of the variable contributions to the determination of the principal components. If a variable contribution turns out to be nonsignificant then the loading associated with this variable is set to zero. This leads to a simplification of principal components in that sense that they can be more easily interpreted. Hypothesis testing is based on a procedure of simulation by permutations of the rows of the data matrix at hand. The interest of this procedure is illustrated using a real data set.