Pca stability studied by the bootstrap and the infinitesimal jackknife method

Abstract

General results are given about the asymptotic convergence of the Infinitesimal Jackknife estimation method. The development until the order four are given. The Infinitesimal Jackknife method is used to give stability index of the results of a PCA. The exact variance of a bootstrapped variance matrix is given. Infinitesimal Jackknife estimates are obtained for the bias and variances of eigenvalues, eigenvectors and stability index for a PCA on a variance or a correlation matrix. The Infinitesimal Jackknife method is compared with the bootstrap on real data