Modified Three-Stage Sampling for Fixed-Width Interval Estimation of the Common Variance of Equicorrelated Normal Distributions

In this work, we present a modified three-stage sampling procedure to construct fixed-width confidence intervals of the common variance of equicorrelated normal distributions. We derive the exact distribution of the stopping variable of this sampling scheme and also the exact distribution of the estimator of the common variance at stopping. The modified three-stage sampling substantially reduces the expected sample size compared to that of the two-stage sampling scheme of Haner and Zacks (2013). The coverage probabilities of the proposed interval estimators are computed exactly and are compared with the coverage probabilities obtained by two-stage sampling. We derive exact formulae for the functionals of the stopping variable and the estimator of the common variance at stopping.