Asymptotic Expansions For Confidence Intervals With Fixed Proportional Accuracy.

When the variance is unknown, the problem of setting fixed width confidence intervals for the mean may not be solvable by a single stage sampling. Then a natural recourse is to use sequential procedures. The asymptotic theory for normal mean has been fully investigated by several authors. However, for non normal case, the sample mean and the estimate of the variance could be highly dependent and expansions of the confidence levels may be difficult to derive and often very complicated to work with in the case where obtainable. In this thesis, the problem of setting confidence intervals with fixed proportional accuracy of the natural parameter of an exponential family is investigated using an approach different from the classical one: instead of the coverage probability at a fixed but arbitrary $\omega$, a collection of average coverage probabilities over $\omega$ in a neighborhood of a fixed but arbitrary $\omega\sb0$ are considered. The performance of both a fully sequential and a three stage procedure is studied. Asymptotic expansions of the average coverage probability and the expected stopping time are obtained in each case and the procedures are shown to perform very well in Monte-Carlo simulation studies.Ph.D.Pure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128115/2/8801374.pd