Bootstrapping the latent roots of certain random matrices

Abstract

Eigenvalues and functions of eigenvalues play an important role in the reduction of the dimensionality of data in multivariate analysis. However, even under the usual normal model context, the associated distributional theory is extremely complicated. In this paper, bootstrap algorithms for ap-proximating the distributions of functions of certain eigenvalues are given, with applications to confidence interval construction for population param-eters. Extensive Monte Carlo simulation results demonstrate the small sample performance of the bootstrap simultaneous confidence sets

Keywords:

• bootstrap
• eigenvalues
• confidence sets
• nonpara-metric inference
• simultaneous inference