Estimation of Error Variance in the Analysis of Experiments Using Two-Level Orthogonal Arrays

Abstract

We consider estimation of an unknown error variance based on the experiments using two-level orthogonal arrays under squared error loss. We address two shrinkage type estimators obtained by pooling sums of squares for factorial effects when they are smaller than the natural estimator or the unbiased one. We discuss whether these two shrinkage estimators uniformly improve upon the natural one or the unbiased one, respectively. It depends on the combination of the number of columns to which the error term is assigned and that of all factorial effects. Through numerical evaluation, we examine the conditions for uniform improvement. Performance of the improved estimators compared with the unbiased estimator is also examined by taking into account both the bias and MSE reduction.

Key Words:

• Stein's estimator
• Uniform improvement
• Pooling

Acknowledgment

The authors are grateful to a referee for insightful and constructive comments.