Multivariate confidence region using quantile vectors

• Published in: Communications for statistical applications and methods Vol. 24; no. 6; pp. 641 - 649
• Main Authors: Hong, Chong Sun, Kim, Hong Il
• Format: Journal Article
• Language: English
• Published: 한국통계학회 01.11.2017
• Subjects: coverage rate; ellipse; ellipsoid; quantile vector; ellipse; quantile vector; coverage rate; ellipsoid
• ISSN: 2287-7843
• DOI: 10.29220/CSAM.2017.24.6.641

Multivariate confidence regions were defined using a chi-square distribution function under a normal as-sumption and were represented with ellipse and ellipsoid types of bivariate and trivariate normal distribution functions. In this work, an alternative confidence region using the multivariate quantile vectors is proposed to define the normal distribution as well as any other distributions. These lower and upper bounds could be ob-tained using quantile vectors, and then the appropriate region between two bounds is referred to as the quantile confidence region. It notes that the upper and lower bounds of the bivariate and trivariate quantile confidence regions are represented as a curve and surface shapes, respectively. The quantile confidence region is obtained for various types of distribution functions that are both symmetric and asymmetric distribution functions. Then, its coverage rate is also calculated and compared. Therefore, we conclude that the quantile confidence region will be useful for the analysis of multivariate data, since it is found to have better coverage rates, even for asymmetric distributions.