University of Illinois Urbana-Champaign

Sequential and Non-Sequential Confidence Intervals With Guaranteed Coverage Probability and Beta-Protection (Estimation, Statistics, Minimaxity)

Juhlin, Kenton Duane

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Description

Title
Sequential and Non-Sequential Confidence Intervals With Guaranteed Coverage Probability and Beta-Protection (Estimation, Statistics, Minimaxity)
Author(s)
Juhlin, Kenton Duane
Issue Date
1985
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Abstract
  • In this thesis we examine several problems related to the construction of one-sided confidence intervals for the mean of a distribution. Let (mu) be the mean (of a normal distribution with variance 1, or of a 1-parameter exponential distribution) and let (phi)((mu)) be a function of (mu). Given error probabilities (alpha) and (beta), we require that the interval I satisfy P(,(mu)) (mu) (ELEM) I (GREATERTHEQ) 1 - (alpha) and P(,(mu)) (phi)((mu)) (ELEM) I (LESSTHEQ) (beta) for all (mu).
  • For some specific problems we study, there are fixed sample size procedures which are solutions. For such procedures we study their minimaxity and admissibility.
  • If no fixed sample size procedure is a solution, we show the existence of sequential procedures which solve the problem. For some of these we provide numerical results which give some measure of how well the procedures perform. We give details of the computational techniques; these have applicability to sequential problems other than the ones we studied.
Graduation Semester
1985
Type of Resource
text
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http://hdl.handle.net/2142/71231

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