Two-stage fixed-width and bounded-width confidence interval estimation methodologies for the common correlation in an equi-correlated multivariate normal distribution

Abstract

In this article, two-stage and fixed sample size procedures are developed for constructing confidence intervals for the common correlation ρ of an equi-correlated multivariate normal distribution. Two different approaches for estimation are considered, namely, fixed-width and bounded-width interval estimation. In the fixed-width confidence interval estimation problem, a two-stage procedure is developed and the exact distribution of the corresponding stopping variable and the exact coverage probability of the interval estimator are derived. Asymptotic optimality properties such as asymptotic first-order efficiency and asymptotic consistency properties of the two-stage procedure are established. Bounded-width confidence intervals are obtained by applying fixed-accuracy estimation methodologies of Mukhopadhyay and Banerjee (2014, 2015a,b) and Banerjee and Mukhopadhyay (2016) using different transformations on ρ. Both fixed sample size and two-stage sampling methodologies for bounded-width confidence interval estimation of $\rho$ are developed incorporating such transformations. Finally, performances of all the procedures are compared via extensive sets of simulation studies.

Keywords:

• Asymptotic consistency
• asymptotic efficiency
• exact computations
• fixed accuracy
• proportional closeness
• simulations
• stopping variable
• two-stage sampling

SUBJECT CLASSIFICATIONS:

• 60G51
• 60K15
• 60K40

Acknowledgments

We are grateful to an Associate Editor and a reviewer for their enthusiastic commentaries.

Additional information

Funding

Shyamal K. De received support from grant MTR/2017/000503 under the MATRICS scheme provided by the Science and Engineering Research Board, government of India.