Some aspects of estimators in analysis of variance Model II.

Abstract

It is well known that the standard estimator for variance components in analysis of variance, Model II, can be a negative with positive probability. In practice, when such an estimator is found to be negative it is taken to be zero. Very little is known about the properties of the corresponding truncated estimator. This thesis investigates the variance and bias of the positive truncated estimator. A method of selecting I, the number of classes, is presented that produces maximum power for a test of the hypothesis that produces maximum power for the test of the hypothesis that = 0 while keeping the variance and bias as small as possible.