Estimation of within Model Parameters in Regression Models with a Nested Error Structure

Abstract

Restricted randomizations, similar to those in split-plot type experiments, often are adapted to assign quantitative treatment factors to experimental units. Such restrictions result in the experiment having a nested error structure. Sufficient conditions are presented under which ordinary least squares (OLS) estimates of regressor parameters are uniformly minimum variance unbiased (UMVU). If one designs experiments so that these conditions are satisfied, the analysis is straightforward and easy. When these conditions are not met, three different estimators of nested regressor parameters are suggested and compared.

Key Words:

• Balanced incomplete block design
• Estimated generalized least squares estimator
• Hypergeometric functions