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

We consider a class of invariant sequential procedures for constructing one-sided and two-sided confidence sets for a parameter γ in R$\sp{k}$, with the property that they have a coverage probability at least 1 - α and probability of covering a certain set of false values at most β. 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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Fakhre-Zakeri, Issa

Contributors dc:contributor

• Awijsmon, Robert,

• Statistics

Identifier

(UMI)AAI8803033

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71501