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Power of the quantile confidence region
Journal of the Korean Data & Information Science Society 2018;29:475-84
Published online March 31, 2018
© 2018 Korean Data and Information Science Society.

Chong Sun Hong1 ∙ Hong Il Kim2 ∙ Min Sub Jung3

123Department of Statistics, Sungkyunkwan University
Correspondence to: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail: cshong@skku.edu
Received February 21, 2018; Revised March 9, 2018; Accepted March 16, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The quantile confidence region (QCR) obtainable for general multivariate distribution functions is compared and analyzed with the multivariate normal confidence region (MCR) defined using normal assumptions. The coverage rate of the QCR is greater than or equal to that of the MCR, but the QCR is expressed over a larger area than the MCR in certain cases. In this study, we obtain the power of the QCR and MCR for multivariate distribution functions, and then we discuss some advantages of the bivariate and trivariate QCR that have a higher power than the MCR. The QCRs for various trivariate normal distributions are represented in three-dimensional space in which the shapes and features of the QCR depend on the characteristics of the corresponding distribution function.
Keywords : Confidence region, coverage rate, normal mixture, power, quantile vector.