Robust simultaneous confidence interval estimation of principal component loadings. - Borlongan, Martin Augustine B. (University of the Philippines, 2015)
Abstract (In principal components analysis, outlying observation cause perturbations in the eigenvectors that consequently influence the principal components (PCs). Estimation of PC loadings are sensitive to outliers and hence, subsequent inference are not optimal. We propose a method that integrates bootstrap into a fully-automated forward search in the construction of robust confidence intervals of for the elements of the eigenvectors of the correlation matrix in the presence of outliers. The coverage probability of the proposed bootstrap simultaneous confidence intervals was compared to the coverage probabilities of regular asymptotic confidence region and asymptotic confidence region via the Minimum Covariance Determinant (MCD) approach through a simulation study. The proposed method generally yielded more stable coverage probabilities for datasets with or without outliers across several sample sizes compared to approaches based on asymptotic results).