Sequential Confidence Intervals for the Common Mean of a set of Heteroscedastic Normal Populations

SYNOPTIC ABSTRACT

Two kinds of sequential procedures are proposed for the construction of fixed-width confidence intervals for the common mean of several normal populations. The first kind is motivated by the solution of the fixed-sample problem with known variances. Thus a sequential procedure is obtained which takes an observation from each population at each stage. The second kind of procedure, which could lead to a considerable savings in observations, first uses a procedure for the selection of the smallest variance. Further observations are then taken only from the selected population. Asymptotic properties and asymptotic relative efficiencies are investigated. Results of a Monte Carlo study indicate agreement between the asymptotic results and the actual behavior of the procedures.

Key words and Phrases:

• sequential procedures
• selection procedures
• asymptotic theory
• maximum likelikhood
• asymptotic efficiency