On the comparison of missing-cell estimates in the designed experiments

Abstract

This paper discusses the application of Murray``s results to other designerd experiments with one missing observation. The classical missing-cell estimate used in the three-way, more higher-way factorial design, or balanced two-stage nested design is unbiased but does not have minimum variance when one or more of factors in these design are considered random. The alternative unbiased least squares estimate of the appropriate cell mean is given, and it has smaller variance when at least one of factors is considered random.