Sequential Confidence Sets With Beta-Protection in the Presence of Nuisance Parameters

Kim, Sung Lai

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Description

Title

Sequential Confidence Sets With Beta-Protection in the Presence of Nuisance Parameters

Author(s)

Kim, Sung Lai

Issue Date

1987

Doctoral Committee Chair(s)

Wijsman, Robert A.,

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Statistics

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.

Graduation Semester

1987

Type of Resource

text

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http://hdl.handle.net/2142/71502

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