## 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

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.

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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