Comparisons of Designs and Estimation Procedures for Estimating Parameters in a Two-Stage Nested Process

For the usual two-stage nested random model, N observations are to be used to estimate some or all of these parameters: μ (the general mean), σ a 2 (the between classes variance component), σ b 2 (the within classes variance component) and ρ = σ a 2/σ b 2 Using the traditional analysis of variance estimator, with fixed number of classes, (k), an allocation procedure to minimize the variance of the estimator is derived to estimate σ a 2 or ρ: p + 1 observations in each of r classes and p observations in each of k − r classes, where N = pk + r, 0 ≤ r 1, p = 1 for σ a 2 and p = 2 for . Investigations on the effect of u...