MINQE for the One-Way Classification

Abstract

The minimum norm quadratic estimator (MINQE), without the condition of unbiasedness, is given for the effect variance of a one-way classification. The computational form is relatively simple with no iteration necessary, and the prior weight is given as a function of the harmonic mean of the numbers of readings per classification. A comparison is made of the mean squared error (MSE) of MINQE and the estimators of Swallow and Monahan (1984) for the layouts of that article. The MSE of MINQE is shown to be smaller than the MSE of these estimators when the effect variance is greater than the error variance. A discussion is also given illustrating a desirable property of a smaller MSE even in the presence of nontrivial bias.

KEY WORDS:

• Variance components
• Mean squared error
• Quadratic estimator