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Title:Sequential and Non-Sequential Confidence Intervals With Guaranteed Coverage Probability and Beta-Protection (Estimation, Statistics, Minimaxity)
Author(s):Juhlin, Kenton Duane
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
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.
Issue Date:1985
Description:142 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985.
Other Identifier(s):(UMI)AAI8511624
Date Available in IDEALS:2014-12-16
Date Deposited:1985

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