The admissibility of some generalized and stepwise Bayes estimators

dc.contributor.author Kim, Byung
dc.contributor.department Statistics
dc.date 2018-08-23T00:33:31.000
dc.date.accessioned 2020-06-30T07:18:09Z
dc.date.available 2020-06-30T07:18:09Z
dc.date.copyright Tue Jan 01 00:00:00 UTC 1985
dc.date.issued 1985
dc.description.abstract <p>Consider an estimation problem in the one parameter exponential family of distributions under squared error loss. Das Gupta and Sinha (1984) and Meeden and Ghosh gave, using an approach given in Brown and Hwang (1982) which is in turn based on Blyth's (1951) method, two different sets of sufficient conditions for admissibility of generalized Bayes estimators of an arbitrary parametric function. These two sets of sufficient conditions are discussed and compared;Also, using Karlin's technique, sufficient conditions are given for generalized Bayes estimators to be admissible under squared error loss for estimating an arbitrary nonnegative, differentiable, strictly increasing or decreasing parametric function in one parameter nonregular families. Some examples are subsequently given;Finally, we consider estimating an arbitrary parametric function in the case when the parameter and sample spaces are countable and the decision space is arbitrary. Using the notions of a stepwise Bayes procedure and finite admissibility, a theorem is proved which shows that every finitely admissible estimator is unique stepwise Bayes. Under an additional assumption, it is shown that the converse is true as well. The first result is also extended to the case when the parameter and sample spaces are arbitrary, i.e., not necessarily countable. In a special setting in which the parameters, sample, and decision spaces are all countable, it is shown that the class of all admissible estimators is exactly the same as that of all finitely admissible estimators.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/12081/
dc.identifier.articleid 13080
dc.identifier.contextkey 6761768
dc.identifier.doi https://doi.org/10.31274/rtd-180813-13359
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/12081
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/65410
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/12081/r_8524671.pdf|||Fri Jan 14 19:12:08 UTC 2022
dc.subject.disciplines Statistics and Probability
dc.subject.keywords Statistics
dc.title The admissibility of some generalized and stepwise Bayes estimators
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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