Jackknife estimation of the eigenvalues of the covariance matrix

Abstract

The properties of the jackknife statistic for the eigenvalues of the covariance and the correlation matrix are studied, using von Mises expansions. Influence functions of the eigenvalues, up to the third order for the covariance matrix, and up to the second order for the correlation matrix, are given. An explicit expression of the infinitesimal jackknife estimator is obtained. It is shown that, for small sample sizes, the jackknife standard error may be a biased estimator of the standard error of the sample eigenvalues. Due to the characteristics of the influence functions, the jackknife eigenvalues and the jackknife standard errors are non-robust estimators. Monte Carlo simulations show that the jackknife eigenvalues are more heavily affected than the sample eigenvalues by contaminations of the data.