Estimators for the One-Way Random Effects Model with Unequal Error Variances

Abstract

Using the random effects model, y_ij = μ + α _i + ∈ _ij , (i = 1, …, k; j = 1, …, n_i ), where α _i and ∈ _ij are normal with means zero and variances σ_α ² and σ _i ², this article considers eight methods of estimating σ _i ², σ_α ², and thirteen corresponding procedures of estimating μ. Biases and mean squared errors (MSE's) of these procedures are examined for variations in the magnitudes of the unknown parameters, the sample sizes, and the number of groups.

Key Words:

• Combining the results of experiments
• Unequal variances and unequal sample sizes
• Estimators for the variances and the mean
• ANOVA and MINQUE type of estimators
• Two-stage procedure
• Biases and mean squared errors