Estimation of multivariate normal mean and its application to mixed linear models

dc.contributor.author Lee, Youngjo
dc.contributor.department Statistics
dc.date 2018-08-15T05:42:40.000
dc.date.accessioned 2020-07-02T06:07:17Z
dc.date.available 2020-07-02T06:07:17Z
dc.date.copyright Sat Jan 01 00:00:00 UTC 1983
dc.date.issued 1983
dc.description.abstract <p>Let X = (x(,1),x(,2),...,x(,p))' be a multivariate normal random variable with mean vector, (theta), in a space (THETA), and variance matrix I;From Strawderman's (1971) class of estimators, we derive a minimax admissible estimator for (theta). It has a relatively simple form when p is greater than or equal to five. We also extend Stein's (1973) technique to evaluate unbiased estimators of risks for discontinuous estimators. Then, we show the exact risks of a preliminary test estimator and of compromised or mixture estimators. We develop estimators that shrink towards some subspace of (THETA) and show the relationship between shrinkage functionals and variance component estimators in balanced mixed linear models. We also investigate the asymptotic behavior of shrinkage estimators. By choosing an appropriate subspace, we show that our estimator and ridge regression estimators achieve stability of prediction in a particular data example;References;Strawderman, W. E. 1971. Proper Bayes Minimax Estimators of the Multivariate Normal Mean. The Annals of Mathematical Statistics 42:385-388. Stein, C. 1973. Estimation of the Mean of a Multivariate Distribution Proceedings of the Prague Symposium on Asymptotic Statistics:345-387.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/8496/
dc.identifier.articleid 9495
dc.identifier.contextkey 6335134
dc.identifier.doi https://doi.org/10.31274/rtd-180813-8589
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/8496
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/81490
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/8496/r_8407095.pdf|||Sat Jan 15 02:12:07 UTC 2022
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Statistics
dc.title Estimation of multivariate normal mean and its application to mixed linear models
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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