Improved estimation of eigen vector of covariance matrix is considered under uncertain
prior information (UPI) regarding the parameter vector. Like statistical models
underlying the statistical inferences to be made, the prior information will be
susceptible to uncertainty and the practitioners may be reluctant to impose the additional
information regarding parameters in the estimation process. A very large
gain in precision may be achieved by judiciously exploiting the information about the
parameters which in practice will be available in any realistic problem.
Several estimators based on preliminary test and the Stein-type shrinkage rules
are constructed. The expressions for the bias and risk of the proposed estimators
are derived and compared with the usual estimators. We demonstrate that how
the classical large sample theory of the conventional estimator can be extended to
shrinkage and preliminary test estimators for the eigenvector of a covariance matrix.
It is established that shrinkage estimators are asymptotically superior to the usual
sample estimators. For illustration purposes, the method is applied to three datasets.
Ahmed, S.E. (2005), Appoximation-assisted estimation of eigenvectors under quadratic loss, Research Letters in the Information and Mathematical Sciences, 8, 77-96