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

Abstract

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.

Keywords:

• Common variance
• Equicorrelated normal
• Exact distribution of stopping variable
• Fixed-width interval estimation
• Three-stage sampling
• Two-stage sampling

Subject Classifications:

• 60G51
• 60K15
• 60K40

ACKNOWLEDGMENTS

The author is eternally grateful to Professor Shelemyahu Zacks for suggesting this problem and for his constant support and guidance throughout this work. The author is thankful to the Editor, Professor Nitis Mukhopadhyay, for his careful review and suggestions that helped improve this article.

Notes

Recommended by Shelly Zacks