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Title:Sequential Confidence Sets With Beta-Protection in the Presence of Nuisance Parameters
Author(s):Kim, Sung Lai
Doctoral Committee Chair(s):Wijsman, Robert A.,
Department / Program:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract:In this thesis we study sequential procedures for constructing one-sided and bounded sequential confidence sets with $\beta$-protection and coverage probability at least 1 $-$ $\alpha$ for the mean of a distribution in the presence of nuisance parameters.
Let $\{X\sb{n}$: n = 1,2, dots,$\}$ be i i d p-variate (p $\geq$ 1) random variables with distribution $P\sb{\theta}$, $\theta\in\Theta$. The parameter space $\Theta$ is some abstract set for which various choices will be made. The mean $\mu$ = $\mu(\theta)$ of $P\sb{\theta}$ is the parameter of interest, the rest of $\theta$ will be regarded as a nuisance parameter. In the simplest case $\mu$ is real valued and there is given an imprecision function $\delta(\mu)$ $>$ 0 and error probabilities 0 $$ 1). In the univariate case several asymptotic properties of the stopping time are obtained in various limiting situations.
Issue Date:1987
Description:56 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987.
Other Identifier(s):(UMI)AAI8803088
Date Available in IDEALS:2014-12-16
Date Deposited:1987

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