On fixed-width simultaneous confidence intervals for multiple comparisons and some related problems

Abstract

This thesis considers inferences about the means of several independently and normally distributed populations with a common variance. The first part discusses the constructions of fixed-width simultaneous confidence intervals when the variance is an unknown parameter by using sequential samplings. A set of fixed-width simultaneous confidence intervals is often used to make simultaneous inferences, with a probability that all the inferences made are simultaneously correct being at least 1 - α, the simultaneous confidence level. Certain probabilities of making simultaneously correct inferences are often larger than the confidence level 1 - α. These are considered in the second part of the thesis. The third and final part of the thesis studies the multiple tests corresponding to the simultaneous confidence intervals. Some new power functions are defined and their properties are investigated.

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