Taeho Kim

Date of Award

Summer 2019

Document Type

Open Access Dissertation



First Advisor

Edsel A. Peña

Second Advisor

Karl Gregory


Multiple interval estimation for a set of parameters is investigated. To begin, a strategy of optimization for a multiple interval estimator (MIE) is introduced. This approach allocates distinct optimized levels to individual interval estimators so that the global expected content can be minimized while the global coverage probability is still maintained at a global level. This optimal allocation is achieved by a decision theoretic procedure which consists of two global risk functions. The major part of this manuscript is devoted to two multiple interval estimation procedures. Both procedures adopt prior information added to the classical setting, but these procedures do not particularly follow the frequentist or Bayesian approach. The first procedure starts from a practical motivation in the use of prior information. That is, a pair of thresholds is established based on the prior information to discard one side of the interval estimators in a particular subset of an MIE. Through this process, the global expected content of the MIE can be reduced. On the other hand, the second procedure also utilizes prior information, but it focuses more on seeking a coherent structure for an MIE which involves a class of heterogeneous parameters. In particular, the prior information is provided in the form of a non-informative prior distribution. Then the resulting MIE can be viewed from both the frequentist and Bayesian perspectives. An appropriate choice of prior distribution is naturally achieved by assigning group structures over the three fundamental components: the sample space, the parameter space, and the action space. Then the right Haar measure provides the form of non-informative prior distribution. In addition, the left Haar measure can also be exploited to evaluate the expected content of the MIE.