Estimating Quantiles of Normal Populations with a Common Mean

• Published in: Communications in statistics. Theory and methods Vol. 40; no. 15; pp. 2719 - 2736
• Main Authors: Kumar, Somesh, Tripathy, Manas Ranjan
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.08.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Common mean; Computer simulation; Equivariant estimators; Estimators; Exact sciences and technology; General topics; Inadmissibility; Linear inference, regression; Mathematical models; Mathematics; Minimaxity; Populations; Probability and statistics; Quantile estimation; Quantiles; Risk comparison; Samples; Sciences and techniques of general use; Statistics; Studies; Transformations; Covariance analysis; Minimaxity; Risk comparison; Gaussian distribution; Statistical estimation; Transformation group; Statistical simulation; Affine transformation; Variance analysis; Mean estimation; Variance; Common mean; Statistical method; Statistical regression; Equivariant estimators; 62C20; Quadratic loss; 62F10; 62C15; Quantile; Inadmissibility; Quantile estimation
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2010.491587

Suppose independent random samples are available from two normal populations with a common mean and unequal variances. Estimation of a quantile of the first population is considered with respect to the quadratic loss. Some new estimators for the quantile are proposed using some previously known estimators of a common mean. Inadmissibility results are proved for estimators which are equivariant under affine and location groups of transformations. Risk values of various estimators of a quantile are compared numerically using a detailed simulation study.