THE CALCULATION OF CONFIDENCE REGIONS FOR EIGENVECTORS

An explicit algorithm is given for constructing a confidence region on the appropriate unit sphere for an eigenvector, given a large sample. It is assumed the eigenvector corresponds to the largest eigenvalue of Exx^T, a matrix with distinct eigenvalues, and that the estimation uses n^-1S?x_ix_ix^T. While the theory is generally applicable, the writer has in mind the special case where ∥x∥= 1 i.e. directional data.