The optimal properties of the principle component estimator. (Chinese. English summary) Zbl 0702.62050
Summary: The purpose of this paper is to investigate the optimality properties of the MSE of the principle component estimator in the class of reduced dimension estimators. It has been proved that the principle component estimator has the \(\mu\)-m, \(\mu\)-P income, loss and \(\mu\)-MB optimality properties. In addition, it has been proved that the principle component estimator is a general best Bayesian estimator of \(\beta\) in the class \({\mathcal D}_ r\).
MSC:
62H12 | Estimation in multivariate analysis |
62H25 | Factor analysis and principal components; correspondence analysis |
62J05 | Linear regression; mixed models |