University of Illinois Urbana-Champaign

Sequential Confidence Sets With Guaranteed Coverage Probability and Beta-Protection in Multiparameter Families

Fakhre-Zakeri, Issa

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https://hdl.handle.net/2142/71501

Description

Title
Sequential Confidence Sets With Guaranteed Coverage Probability and Beta-Protection in Multiparameter Families
Author(s)
Fakhre-Zakeri, Issa
Issue Date
1987
Doctoral Committee Chair(s)
Awijsmon, Robert,
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
We consider a class of invariant sequential procedures for constructing one-sided and two-sided confidence sets for a parameter $\gamma$ in R$\sp{k}$, with the property that they have a coverage probability at least 1 - $\alpha$ and probability of covering a certain set of false values at most $\beta$. In addition, a method is proposed that is capable of generating a wide variety of sequential confidence sets (not necessarily equivariant) and some of its properties are investigated. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random variable and for its multivariate analogue.
Graduation Semester
1987
Type of Resource
text
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http://hdl.handle.net/2142/71501

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