Research Letters in the Information and Mathematical Sciences

Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/4332

Research Letters welcomes papers from staff and graduate students at Massey University in the areas of: Computer Science, Information Science, Mathematics, Statistics and the Physical and Engineering Sciences. Research letters is a preprint series that accepts articles of completed research work, technical reports, or preliminary results from ongoing research. After editing, articles are published online and can be referenced, or handed out at conferences. Copyright remains with the authors and the articles can be used as preprints to academic journal publications or handed out at conferences. Editors Dr Elena Calude Dr Napoleon Reyes The guidelines for writing a manuscript can be accessed here.

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Subject: search.filters.subject.Estimation process

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    Appoximation-assisted [sic] estimation of eigenvectors under quadratic loss
    (Massey University, 2005) Ahmed, S.E.
    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.